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The structure of compact linear operators in Banach spaces

在 Banach 空格的紧缩的线性操作符的结构

作     者:Edmunds, D. E. Evans, W. D. Harris, D. J. 

作者机构:Univ Sussex Dept Math Brighton BN1 9QH E Sussex England Cardiff Univ Sch Math Cardiff CF24 4AG S Glam Wales 

出 版 物:《REVISTA MATEMATICA COMPLUTENSE》 (孔普卢顿数学杂志)

年 卷 期:2013年第26卷第2期

页      面:445-469页

核心收录:

学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主  题:Compact linear operators Strictly convex Banach spaces Approximation property Basis 

摘      要:In Edmunds et al. [J Lond Math Soc 78(2):65-84, 2008], a representation of a compact linear operator T acting between reflexive Banach spaces X and Y with strictly convex duals was established in terms of elements x(n) is an element of X projections P-n of X onto subspaces X-n which are such that boolean AND X-n = kerT and linear projections S-n satisfying S(n)x = Sigma(n-1)(j=1) xi(j)(x)x(j) where the coefficients xi(j)(x) are given explicitly. If kerT = {0} and the condition (A): sup parallel to S-n parallel to infinity is satisfied, the representation reduces to an analogue of the Schmidt representation of T when X and Y are Hilbert spaces, and also (x(n)) is a Schauder basis of X;thus condition (A) can not be satisfied if X does not have the approximation property. In this paper we investigate circumstances in which (A) does or does not hold, and analyse the implications.

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