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An Introduction to the Theory of C~*-modules
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作者 邓宏钧 刘德权 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第2期72-77,共6页
This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ... This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them. 展开更多
关键词 commutative c~*-algebra c~*-module c~*-homomorphism
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面向软件定义的C~4ISR系统资源建模方法研究 被引量:2
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作者 张兆晨 毛少杰 +1 位作者 闫晶晶 毛晓彬 《现代防御技术》 北大核心 2024年第1期65-73,共9页
为实现马赛克化的C~4ISR系统构建模式,瞄准系统“元要素”构建,以软件定义技术为驱动,探讨了可定义的资源建模原理,提出了资源建模过程,定义了C~4ISR系统资源概念内涵,基于多视角建立了资源分类框架;围绕资源信息流受控和能力开放共享,... 为实现马赛克化的C~4ISR系统构建模式,瞄准系统“元要素”构建,以软件定义技术为驱动,探讨了可定义的资源建模原理,提出了资源建模过程,定义了C~4ISR系统资源概念内涵,基于多视角建立了资源分类框架;围绕资源信息流受控和能力开放共享,提出了模型要素,针对7类资源特点建立了参考模型。通过典型案例下资源实例化建模,验证了模型对软件定义的系统构建的适用性。 展开更多
关键词 软件定义 c~4ISR系统 资源模型 马赛克 能力开放 受控使用
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The characterization of a class of quantum Markov semigroups and the associated operator-valued Dirichlet forms based on Hilbert C~*-module l_2(A) 被引量:3
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作者 ZHANG LunChuan GUO MaoZheng 《Science China Mathematics》 SCIE 2014年第2期377-387,共11页
We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we intr... We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form. 展开更多
关键词 Hilbert C*-module quantum Markov semigroup operator-valued Dirichlet forms
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Derivations on the Algebra of Operators in Hilbert C~*-Modules 被引量:2
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作者 Peng Tong LI De Guang HAN Wai Shing TANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第8期1615-1622,共8页
Let M be a full Hilbert C*-module over a C*-algebra A, and let End^(.A4) be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End*A(M) is an inner ... Let M be a full Hilbert C*-module over a C*-algebra A, and let End^(.A4) be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End*A(M) is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on "compact" operators completely decides innerness of derivations on EndA(M). If .4 is unital (no commutativity is assumed) such that every derivation of A is inner, then it is proved that every derivation of EndA(Ln(A)) is also inner, where Ln(A) denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA(M) which behave like derivations when acting on zero products. 展开更多
关键词 DERIVATIONS inner derivations C*-algebras Hilbert C*-modules
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HILBERT C~*-MODULES AND THEIR BOUNDED MODULE MAPS
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作者 林华新 《Science China Mathematics》 SCIE 1991年第12期1409-1421,共13页
Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "c... Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "compact" module maps on E. In the case that A isinfinitely dimensional primitive C~*-algebra, E is shown to be self-dual if and only if E isalgebraically finitely generated. 展开更多
关键词 HILBERT MODULES c~*-algebra MODULE map.
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Compatibility and Schur Complements of Operators on Hilbert C~*-Module
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作者 Xiaochun FANG Jing YU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2011年第1期69-88,共20页
Let E be a Hilbert C*-module,and Y be an orthogonally complemented closed submodule of E.The authors generalize the definitions of Y-complementability and Y-compatibility for general(adjointable) operators from Hil... Let E be a Hilbert C*-module,and Y be an orthogonally complemented closed submodule of E.The authors generalize the definitions of Y-complementability and Y-compatibility for general(adjointable) operators from Hilbert space to Hilbert C*-module,and discuss the relationship between each other.Several equivalent statements about Y-complementability and Y-compatibility,and several representations of Schur complements of Y-complementable operators(especially,of Y-compatible operators and of positive Y-compatible operators) on a Hilbert C*-module are obtained.In addition,the quotient property for Schur complements of matrices is generalized to the quotient property for Schur complements of Y-complementable operators and Y*-complementable operators on a Hilbert C*-module. 展开更多
关键词 Hilbert C*-module Compatibility Complementability Schur complement Quotient property
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A generalization of co-*~n-modules
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作者 姚玲玲 陈建龙 《Journal of Southeast University(English Edition)》 EI CAS 2010年第3期505-508,共4页
A module is called a co-*∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-*∞-module, the functor Hom RU(-,U)is exact in Copre... A module is called a co-*∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-*∞-module, the functor Hom RU(-,U)is exact in Copres∞(U). A module U is a co-*∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞(U) and I is a set, N∈Copres∞(U) is equivalent to Ext1R(N,U)→Ext1R(UI,U) is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞(U), N∈Copres∞(U) is equivalent to the induced sequence 0→Δ(N)→Δ(M)→Δ(L)→0 which is exact if and only if U induces a duality ΔUS:⊥USCopres∞(U):ΔRU. Moreover, U is a co-*n-module if and only if U is a co-*∞-module and Copres∞(U)=Copresn(U). 展开更多
关键词 co-*∞-module ∞-quasi-injective co-selfsmall co-*n-module
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STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE FUNCTIONAL EQUATION 被引量:2
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作者 Ali Ebadian Ismail Nikoufar +1 位作者 Themistocles M.Rassias Norouz Ghobadipour 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1226-1238,共13页
In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen... In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf(x+y/r)+sg(x-y/s)=2h(x)for r, s ∈ R / {0} on Hilbert C*-modules, where f, g, and h are mappings from a Hilbert C*-module M to M. 展开更多
关键词 Hyers-Ulam-Rassias stability Hilbert C*-module generalized derivation fixed point
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A New Characterization on g-frames in Hilbert C^*-Modules 被引量:1
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作者 Xiang Zhong-qi 《Communications in Mathematical Research》 CSCD 2017年第2期129-134,共6页
In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some pr... In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules(in Chinese). Acta Math. Sinica, 2011, 54(1): 1–8.). 展开更多
关键词 Hilbert C*-module G-FRAME characterization
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The characterization of Γ-modules in terms of fuzzy soft Γ-submodules 被引量:1
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作者 ZHOU Min XIANG Da-jing ZHAN Jian-ming 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第2期217-239,共23页
In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the con... In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of(R,S)-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper. 展开更多
关键词 Fuzzy soft set Γ-module (∈ γ γ q δ)(resp. (■ γ γ δ))-fuzzy soft left R-Γ-submodule(right R-Γ-submodules (R S)-bi-Γ-submodule quasi-Γ-submodule) regular Γ-module
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CHAIN CONDITIONS FOR C*-ALGEBRAS COMING FROM HILBERT C*-MODULES 被引量:1
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作者 Mahmood POURGHOLAMHOSSEIN Mohammad ROUZBEHANI Massoud AMINI 《Acta Mathematica Scientia》 SCIE CSCD 2018年第4期1163-1173,共11页
In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes... In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation. 展开更多
关键词 Hilbert C*-module Noetherian and Artinian C*-algebras purely infinite C*-algebras Morita equivalence
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Rudiment of weak Doi-Hopf π-modules
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作者 贾玲 李方 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第B08期144-154,共11页
The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (Boehm, 2000), also as a generalization of a Doi-... The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (Boehm, 2000), also as a generalization of a Doi-Hopfπ-module introduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules. 展开更多
关键词 Weak semi-Hopf π-coalgebra Weak Doi-Hopf π-modules
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Extended l*-Module
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作者 NIU Yu-qi MENG Xiao-ran YUAN Jian 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第3期390-398,共9页
Theory of uncertainty reasoning base on l-module of true value field,in this paper,an extended l-module was proposed,some properties and lattice measure were discussed,then the lattice integral on l-module was gained.
关键词 true value field l*-module lattice measure lattice integral
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QED-Lie Algebra and Their &pound;-Modules in Superconductivity
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作者 Francisco Bulnes 《Journal of Applied Mathematics and Physics》 2015年第4期417-427,共11页
It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrod... It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrodynamics theory of the TQFT, and the Universe based in lines and twistor bundles to the obtaining of irreducible unitary representations of the Lie groups SO(4) ?andO(3,1) , based in admissible representations of U(1) , and SU(n)? . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of £-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements. 展开更多
关键词 Electromagnetic Representation Electro-Physics Theory LIE Algebra -modules
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Pseudo Frame Decompositions in a Hilbert C*-module H
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作者 YAO Xi-yan 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期276-281,共6页
In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C*-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to eac... In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C*-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using .A-valued linear bounded operator U : H → l^2(.A), V*U = I, a coustructing method of dual weak frame {xj^* : j ∈ H} for a given weak frame {Xj : j ∈ J} is obtained. Moreover, pseudo frame decompositions for 74 is given. 展开更多
关键词 C*-algebra Hilbert C*-module frame dual frame frame decomposition
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C~*-代数上的非负矩阵与正定矩阵 被引量:3
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作者 曹怀信 成波 宁刚 《咸阳师范学院学报》 1999年第3期1-5,共5页
研究C*-代数上矩阵的非负性、可逆性与正定性,应用分块矩阵的技巧,得到了非负矩阵的一系列判别法。同时,研究了矩阵可逆性的判定问题,在此基础上给出了正定矩阵的判别方法.
关键词 c~*-代数 非负矩阵 可逆矩阵 正定矩阵
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纯无限单C~*-代数的扩张代数的K-理论Ⅱ 被引量:1
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作者 刘树冬 方小春 《数学年刊(A辑)》 CSCD 北大核心 2009年第3期433-438,共6页
给出了有单位元的纯无限单的C^*一代数A通过Κ的扩张代数E的K-理论的一种刻画.证明了K0(E)同构于E中所有具有无限余投影的无限投影的Murry—von Neumann等价类全体所成的交换群,它还同构于上述投影的同伦等价类或酉等价类全体所成... 给出了有单位元的纯无限单的C^*一代数A通过Κ的扩张代数E的K-理论的一种刻画.证明了K0(E)同构于E中所有具有无限余投影的无限投影的Murry—von Neumann等价类全体所成的交换群,它还同构于上述投影的同伦等价类或酉等价类全体所成的交换群.还证明了对扩张代数E中的任一满的正元a,存在元索x∈E,使得x^*ax=1,其中Κ为可分无限维Hilbert空间上紧算子全体所成的C^*-代数. 展开更多
关键词 c~*-代数 扩张 K-理论 纯无限
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强无限C~*-代数的性质(英文)
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作者 梁月亮 《华东师范大学学报(自然科学版)》 CAS CSCD 北大核心 2013年第1期104-114,共11页
给出C*-代数迹极限的等价形式,从正元的角度提出强无限C*-代数的概念.研究了强无限C*-代数与纯无限C*-代数之间的基本关系,具有SP-性质的强无限C*-代数的迹极限为强无限的.对于实秩零的C*-代数A而言,若闭双边理想I及商代数A/I为... 给出C*-代数迹极限的等价形式,从正元的角度提出强无限C*-代数的概念.研究了强无限C*-代数与纯无限C*-代数之间的基本关系,具有SP-性质的强无限C*-代数的迹极限为强无限的.对于实秩零的C*-代数A而言,若闭双边理想I及商代数A/I为强无限的,则A为强无限的.具有SP-性质的强无限C*-代数的非零的闭双边理想为强无限的.一个强无限C*-代数的有限直和仍然是强无限的. 展开更多
关键词 纯无限c~*-代数 迹极限 SP-性质
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C~*PCP与(w~*-w)CPCP的关系
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作者 叶远灵 《华南师范大学学报(自然科学版)》 CAS 1996年第4期96-100,共5页
本文证明了下面2个结果:(1)当X*具有PCP时,C*PCP与(w*-w)CPCP等价;(2)X*具有C*PCP当且仅当X*具有(w*-w)CPCP且对X*的每个非空w*-紧凸子集K,(w*-w)PC(K)含有K的... 本文证明了下面2个结果:(1)当X*具有PCP时,C*PCP与(w*-w)CPCP等价;(2)X*具有C*PCP当且仅当X*具有(w*-w)CPCP且对X*的每个非空w*-紧凸子集K,(w*-w)PC(K)含有K的一个w*-稠密G子集. 展开更多
关键词 PCP c~*PCP (w~*-w)CPCP w~*-huskable 强可数完全正则
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Some Inequalities about the Positive Elements in C~*-Algebra
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作者 汪远征 黄学维 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第2期29-31,共3页
In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
关键词 c~*-Algebra positive element
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