On linear operators with p-nuclear adjoints

If \(p\in [1,+\infty]\) and \(T\) is a linear operator with \(p\)-nuclear adjoint from a Banach space \( X\) to a Banach space \(Y\) then if one of the spaces \(X^*\) or \(Y^{***}\) has the approximation property, then \(T\) belongs to the ideal \(N^p\) of operators which can be factored through dia...

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Bibliographic Details
Published in:arXiv.org 2001-07
Main Author: Reinov, Oleg I
Format: Article
Language:English
Subjects:
Adjoints
Banach spaces
Linear operators
Online Access:Get full text
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Summary:If \(p\in [1,+\infty]\) and \(T\) is a linear operator with \(p\)-nuclear adjoint from a Banach space \( X\) to a Banach space \(Y\) then if one of the spaces \(X^*\) or \(Y^{***}\) has the approximation property, then \(T\) belongs to the ideal \(N^p\) of operators which can be factored through diagonal oparators \(l_{p'}\to l_1.\) On the other hand, there is a Banach space \(W\) such that \(W^{**}\) has a basis and such that for each \(p\in [1,+\infty], p\neq 2,\) there exists an operator \(T: W^{**}\to W\) with \(p\)-nuclear adjoint that is not in the ideal \(N^p,\) as an operator from \(W^{**}\) to \( W.\)
ISSN:2331-8422