A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor r...A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor ratios μpGEp/GMpand μnGEn/GMn. A quantitative description is obtained, assuming a mixing of a scalar bound state of 3(f f¯)fstructure with its corresponding vector (f f¯)fstate (f indicating massless elementary fermions). Only a few parameters are needed, mainly fixed by energy and momentum conservation. The nucleon stability is explained by an extra binding in the confinement potential, negative for electric and positive for magnetic binding of the proton, and opposite for the neutron. The stronger electric extra binding of the proton allows a decay of the neutron to proton and electron.展开更多
We show that if a bounded linear operator can be approximated by a net(or sequence)of uniformly bounded finite rank Lipschitz mappings pointwisely,then it can be approximated by a net(or sequence)of uniformly bounded ...We show that if a bounded linear operator can be approximated by a net(or sequence)of uniformly bounded finite rank Lipschitz mappings pointwisely,then it can be approximated by a net(or sequence)of uniformly bounded finite rank linear operators under the strong operator topology.As an application,we deduce that a Banach space has an(unconditional)Lipschitz frame if and only if it has an(unconditional)Schauder frame.Another immediate consequence of our result recovers the famous Godefroy-Kalton theorem(Godefroy and Kalton(2003))which says that the Lipschitz bounded approximation property and the bounded approximation property are equivalent for every Banach space.展开更多
Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known...Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.展开更多
In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP....In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p.展开更多
Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contain...Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.展开更多
We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach spac...We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach space X has the approximation property with respect to Ad whenever X＊ has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.展开更多
文摘A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor ratios μpGEp/GMpand μnGEn/GMn. A quantitative description is obtained, assuming a mixing of a scalar bound state of 3(f f¯)fstructure with its corresponding vector (f f¯)fstate (f indicating massless elementary fermions). Only a few parameters are needed, mainly fixed by energy and momentum conservation. The nucleon stability is explained by an extra binding in the confinement potential, negative for electric and positive for magnetic binding of the proton, and opposite for the neutron. The stronger electric extra binding of the proton allows a decay of the neutron to proton and electron.
基金supported by National Natural Science Foundation of China(Grant Nos.11671214,11971348 and 12071230)Hundred Young Academia Leaders Program of Nankai University(Grant Nos.63223027 and ZB22000105)+2 种基金Undergraduate Education and Teaching Project of Nankai University(Grant No.NKJG2022053)National College Students'Innovation and Entrepreneurship Training Program of Nankai University(Grant No.202210055048)supported by Simons Foundation(Grant No.585081)。
文摘We show that if a bounded linear operator can be approximated by a net(or sequence)of uniformly bounded finite rank Lipschitz mappings pointwisely,then it can be approximated by a net(or sequence)of uniformly bounded finite rank linear operators under the strong operator topology.As an application,we deduce that a Banach space has an(unconditional)Lipschitz frame if and only if it has an(unconditional)Schauder frame.Another immediate consequence of our result recovers the famous Godefroy-Kalton theorem(Godefroy and Kalton(2003))which says that the Lipschitz bounded approximation property and the bounded approximation property are equivalent for every Banach space.
基金supported by the National Natural Science Foundation of China(Grant No.11971403)the Natural Science Foundation of Fujian Province of China(Grant No.2019J01024)。
文摘Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.10526034 and 10701063)the Fundamental Research Funds for the Central Universities(Grant No.2011121039)supported by NSF(Grant Nos.DMS-0800061 and DMS-1068838)
文摘In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p.
基金Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No 20060402)
文摘Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.
基金supported by the Natural Science Foundation of Fujian Province of China(Grant No.2015J01026)supported by the NSF of China(Grant No.11301285)
文摘We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach space X has the approximation property with respect to Ad whenever X＊ has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.
