Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only i...Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.展开更多
Let F be a field of characteristic not 2 and 3.Let f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=BATB.In this paper,we give the...Let F be a field of characteristic not 2 and 3.Let f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=BATB.In this paper,we give the sufficient and necessary condition for f to be such a map.展开更多
The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as wel...The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.展开更多
Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（...Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（x）＋f（y）＋2f（z）（0.3）for all x, y, z ∈ X, then the mapping f ： X →Y is Cauchy additive. Furthermore, we prove the Cauchy-Rassias stability of the functional equations （0.1）, （0.2） and （0.3） in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras.展开更多
Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves simil...Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.展开更多
In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive ...In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.展开更多
We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral fu...We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.展开更多
We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective ...We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.展开更多
The additive mappings that preserve the minimal rank on the algebra of all n × n upper triangular matrices over a field of characteristic 0 are characterized.
Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ...Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ＋ n）, we characterize the additive maps d： L → R satisfying d（um＋n＋1） = （m -＋n ＋ 1）umd（u）un （resp., d（um＋n＋l） = umd（u）un） for all u ∈ L.展开更多
In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set...In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set-valued map.展开更多
In this paper, we discuss the unique existent problems of a additive selection map for the following map F:X→P0(Y):F(r∑i=1αixi)■r∑i=1αiF(xi),■xi∈K,i=1, ··· , r,where αi and αi (i = 1, ·&#...In this paper, we discuss the unique existent problems of a additive selection map for the following map F:X→P0(Y):F(r∑i=1αixi)■r∑i=1αiF(xi),■xi∈K,i=1, ··· , r,where αi and αi (i = 1, ··· , r) are all non-negative real numbers.展开更多
In this paper, we will construct a new class of subadditive set-valued maps and use Cantor theorem to prove that the set-valued map has an unique additive selection map when the set-valued map satisfies some certain c...In this paper, we will construct a new class of subadditive set-valued maps and use Cantor theorem to prove that the set-valued map has an unique additive selection map when the set-valued map satisfies some certain conditions, and then compare the obtained result with the well-known results.展开更多
Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices w...Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.展开更多
In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f（2x ＋ y） ＋ f（2x- y） = 2f（2x） ＋ 2f（x ＋ y） ＋ 2f（x- y）- 4f（x）- f（y）- f（-y）...In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f（2x ＋ y） ＋ f（2x- y） = 2f（2x） ＋ 2f（x ＋ y） ＋ 2f（x- y）- 4f（x）- f（y）- f（-y）deriving from additive, quadratic and cubic mappings on Banach spaces.展开更多
For a Banach algebra A, we denote by .A＊ and .A＊＊ the first and the second duals of A respectively. Let T be a mapping from .A＊ to itself. In this article, we will investigate some stability results concerning the...For a Banach algebra A, we denote by .A＊ and .A＊＊ the first and the second duals of A respectively. Let T be a mapping from .A＊ to itself. In this article, we will investigate some stability results concerning the equations T（αf ＋ βg） -= αT（f） ＋ βT（g）, T（af） = aT（f） andT（αf ＋βg） ＋ T（αf - βg） =- 2α2T（f） ＋ 2β2T（g） where f, g e .A＊, a ∈ A, and α,β ∈ Q ／ {0}.展开更多
In this paper, we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is...In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.展开更多
The high temperature deformation behaviors and thermal workability of Cu_（43）Zr_（48）Al_9 and（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glasses in the supercooled liquid region were investigated by the unia...The high temperature deformation behaviors and thermal workability of Cu_（43）Zr_（48）Al_9 and（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glasses in the supercooled liquid region were investigated by the uniaxial compression tests. The results showed that the high temperature deformation behaviors were highly sensitive to strain rate and temperature, and the flow stress decreased with the increase of temperature, as well as with the decrease of strain rate. Additionally, the（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glass displayed smaller flow stress under the same condition. The flow behavior changed from Newtonian to non-Newtonian with increase of the strain rate, as well as the decrease of temperature, which could be explained by the transition state theory. We found that（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glass had better flow behavior than the Cu_（43）Zr_（48）Al_9 bulk metallic glass in the supercooled liquid region. In addition, the processing maps of the two bulk metallic glasses were constructed considering the power dissipation efficiency. The optimum domain for thermal workability of the bulk metallic glass was located using the processing map, where the power dissipation efficiency was larger than 0.8. It was shown that the（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glass, which had larger area of optimum domain, had excellent thermoplastic forming.展开更多
基金The NSF(11371233)of Chinathe Fundamental Research Funds(GK201301007)for the Central Universities
文摘Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.
文摘Let F be a field of characteristic not 2 and 3.Let f:Mmn(F)→Mmn(F)be an additive map preserving{1,2,T}-inverse,i.e.f(A)=f(A)f(B)Tf(A),f(B)=f(B)f(A)Tf(B)for any A,B C Mmn(F)with A=ABTA,B=BATB.In this paper,we give the sufficient and necessary condition for f to be such a map.
基金The second author is supported by the Science and Engineering Research Board(SERB)of India(MTR/2020/000534).
文摘The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.
基金Supported by Korea Research Foundation Grant KRF-2005-070-C00009
文摘Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（x）＋f（y）＋2f（z）（0.3）for all x, y, z ∈ X, then the mapping f ： X →Y is Cauchy additive. Furthermore, we prove the Cauchy-Rassias stability of the functional equations （0.1）, （0.2） and （0.3） in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras.
文摘Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.
基金Supported by National Natural Science Foundation of China(Grant Nos.11301384,11371201,11201337 and11201338)
文摘In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.
基金Natural Science Foundation of ChinaGrant for Returned Scholars of Shanxi
文摘We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.
基金supported in part by a grant from the Ministry of Science of Slovenia
文摘We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10771157 10871111)Research Grant to Returned Scholars of Shanxi Province (Grant No.2007-38)
文摘The additive mappings that preserve the minimal rank on the algebra of all n × n upper triangular matrices over a field of characteristic 0 are characterized.
文摘Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ＋ n）, we characterize the additive maps d： L → R satisfying d（um＋n＋1） = （m -＋n ＋ 1）umd（u）un （resp., d（um＋n＋l） = umd（u）un） for all u ∈ L.
基金Supported by Science Foundation of Education Committee of Jilin Province of China([2011]No.434)
文摘In this paper, we consider the following subadditive set-valued map F ： X→P0（Y） ：where r and s are two natural numbers. And we discuss the existence and unique problem of additive selection maps for the above set-valued map.
基金Foundation item： Supported by the Science Foundation of Education Committee of Jilin Province（[2011] No434）
文摘In this paper, we discuss the unique existent problems of a additive selection map for the following map F:X→P0(Y):F(r∑i=1αixi)■r∑i=1αiF(xi),■xi∈K,i=1, ··· , r,where αi and αi (i = 1, ··· , r) are all non-negative real numbers.
基金Supported by the National Natural Science Foundation of China（11361064）
文摘In this paper, we will construct a new class of subadditive set-valued maps and use Cantor theorem to prove that the set-valued map has an unique additive selection map when the set-valued map satisfies some certain conditions, and then compare the obtained result with the well-known results.
文摘Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.
基金Supported by National Natural Science Foundation of China(Grant No.11371222)Natural Science Foundation of Shandong Province(Grant No.ZR2012AM024)China Scholarship Council
文摘In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f（2x ＋ y） ＋ f（2x- y） = 2f（2x） ＋ 2f（x ＋ y） ＋ 2f（x- y）- 4f（x）- f（y）- f（-y）deriving from additive, quadratic and cubic mappings on Banach spaces.
文摘For a Banach algebra A, we denote by .A＊ and .A＊＊ the first and the second duals of A respectively. Let T be a mapping from .A＊ to itself. In this article, we will investigate some stability results concerning the equations T（αf ＋ βg） -= αT（f） ＋ βT（g）, T（af） = aT（f） andT（αf ＋βg） ＋ T（αf - βg） =- 2α2T（f） ＋ 2β2T（g） where f, g e .A＊, a ∈ A, and α,β ∈ Q ／ {0}.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671013 and11171022)
文摘In this paper, we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation
文摘In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.
基金supported by the Education Department of Shaanxi Province(14JK1351)the Principal Fund of Xi’an Technological University(0852-302021407)
文摘The high temperature deformation behaviors and thermal workability of Cu_（43）Zr_（48）Al_9 and（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glasses in the supercooled liquid region were investigated by the uniaxial compression tests. The results showed that the high temperature deformation behaviors were highly sensitive to strain rate and temperature, and the flow stress decreased with the increase of temperature, as well as with the decrease of strain rate. Additionally, the（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glass displayed smaller flow stress under the same condition. The flow behavior changed from Newtonian to non-Newtonian with increase of the strain rate, as well as the decrease of temperature, which could be explained by the transition state theory. We found that（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glass had better flow behavior than the Cu_（43）Zr_（48）Al_9 bulk metallic glass in the supercooled liquid region. In addition, the processing maps of the two bulk metallic glasses were constructed considering the power dissipation efficiency. The optimum domain for thermal workability of the bulk metallic glass was located using the processing map, where the power dissipation efficiency was larger than 0.8. It was shown that the（Cu_（43）Zr_（48）Al_9）_（98）Y_2 bulk metallic glass, which had larger area of optimum domain, had excellent thermoplastic forming.
