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A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES 被引量:3
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作者 王紫 王玉文 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1619-1631,共13页
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma"... In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces. 展开更多
关键词 Banach space bounded linear operator metric projection generalized inverse perturbation analysis Moore-Penrose quasi-additive
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Asymptotically Isometric Copy of l~β(0<β<1) in Spacesof Bounded Linear Operators
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作者 Chen ZHI Mei Mei SONG 《Journal of Mathematical Research and Exposition》 CSCD 2011年第3期562-566,共5页
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
关键词 asymptotically isometric copy space of bounded linear operators quotient space fixed point property.
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Some Remarks on Operators and Their Conjugates
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作者 陈滋利 张静 《Journal of Southwest Jiaotong University(English Edition)》 2010年第4期346-348,共3页
We first characterize the range spaces F for which {T':T∈K(E,F)}=K(F',E') holds for all Banach spaces E. Then we present some sufficient conditions for the equality T'=T'. Some related results are also incl... We first characterize the range spaces F for which {T':T∈K(E,F)}=K(F',E') holds for all Banach spaces E. Then we present some sufficient conditions for the equality T'=T'. Some related results are also included. 展开更多
关键词 Banach space AM-space bounded linear operator CONJUGATE AM-compact operator
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Several Norms of Operators on Banach Lattices
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作者 Li Jie(李捷) +1 位作者 Chen Zili(陈滋利) 《Journal of Southwest Jiaotong University(English Edition)》 2002年第2期130-133,共4页
We present some positive results involving the several norms of operators on Banach lattices, which shows several relations of these operator norms.
关键词 Banach lattice bounded linear operator r-norm k-norm.
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Generalized regular points of a C^1 map between Banach spaces
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作者 史平 马吉溥 《Journal of Southeast University(English Edition)》 EI CAS 2007年第1期148-150,共3页
Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applicatio... Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applications in nonlinearity and global analysis. We characterize the generalized regular points of f using the three integer-valued (or infinite) indices M(x0), Mc(x0) and Mr(x0) at x0 ∈ E generated by f and by analyzing generalized inverses of bounded linear operators on Banach spaces, that is, iff '(x0) has a generalized inverse in the Banach space B(E, F) of all bounded linear operators on E into F and at least one of the indices M(x0), Mc(x0) and Mr(x0) is finite, then xo is a generalized regular point off if and only if the multi-index (M(x), Me(x), Mr(x)) is continuous at X0. 展开更多
关键词 Banach space bounded linear operator generalized inverse index generalized regular point semi- Fredholm mao
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THE METRIC GENERALIZED INVERSE AND ITS SINGLE-VALUE SELECTION IN THE PRICING OF CONTINGENT CLAIMS IN AN INCOMPLETE FINANCIAL MARKET
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作者 Zi WANG Xiaoling WANG Yuwen WANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第4期1681-1689,共9页
This article continues to study the research suggestions in depth made by M.Z.Nashed and G.F.Votruba in the journal"Bull.Amer.Math.Soc."in 1974.Concerned with the pricing of non-reachable"contingent cla... This article continues to study the research suggestions in depth made by M.Z.Nashed and G.F.Votruba in the journal"Bull.Amer.Math.Soc."in 1974.Concerned with the pricing of non-reachable"contingent claims"in an incomplete financial market,when constructing a specific bounded linear operator A:l_(1)^(n)→l_(2) from a non-reflexive Banach space l_(1)^(n) to a Hilbert space l_(2),the problem of non-reachable"contingent claims"pricing is reduced to researching the(single-valued)selection of the(set-valued)metric generalized inverse A■ of the operator A.In this paper,by using the Banach space structure theory and the generalized inverse method of operators,we obtain a bounded linear single-valued selection A^(σ)=A+of A■. 展开更多
关键词 Incomplete financial market bounded linear operator metric generalized inverse single-value selection Moore-Penrose generalized inverse
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SOME RESULTS RELATED TO THE SEPARABLE QUOTIENT PROBLEM
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作者 钟怀杰 《Acta Mathematica Scientia》 SCIE CSCD 1996年第3期248-256,共9页
The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimens... The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed. 展开更多
关键词 Banach space separable space quotient space bounded linear operator
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On Absolute N?rlund Spaces and Matrix Operators
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作者 G.Canan HAZAR M.Ali SARIG?L 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第5期812-826,共15页
In a more recent paper, the second author has introduced a space |Cα|k as the set of all series by absolute summable using Cesaro matrix of order α 〉 -1. In the present paper we extend it to the absolute NSrlund ... In a more recent paper, the second author has introduced a space |Cα|k as the set of all series by absolute summable using Cesaro matrix of order α 〉 -1. In the present paper we extend it to the absolute NSrlund space |Np^θ|k taking Norlund matrix in place of Cesaro matrix, and also examine some topological structures, α-β-γ-duals and the Schauder base of this space. Further we characterize certain matrix operators on that space and determine their operator norms, and so extend some well-known results. 展开更多
关键词 Sequence spaces absolute Norlund summability dual spaces matrix transformations bounded linear operator BK spaces
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Some New Results Related to Compact Matrix Operators in the Class((l_p)T,l_∞)
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作者 Katarina PETKOVI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第8期1339-1347,共9页
The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈((lp)T,l∞), where T is an arbitrary triangle, 1 ≤ p ≤∞, to be a compact operator. In the past,only sufficient co... The main goal of this paper is to establish necessary and sufficient conditions for a matrix A ∈((lp)T,l∞), where T is an arbitrary triangle, 1 ≤ p ≤∞, to be a compact operator. In the past,only sufficient conditions were established in almost all of those cases, by using the Hausdorff measure of noncompactness. We improve those results by applying another method for the characterizations of compact linear operators between BK spaces. 展开更多
关键词 BK spaces bounded and compact linear operators Hausdorff measure of noncompactness
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