Complementably universal Banach spaces, II

W. B. Johnson; A. Szankowski

doi:10.1016/j.jfa.2009.07.008

Complementably universal Banach spaces, II

W. B. Johnson^*, A. Szankowski

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The two main results are: A.If a Banach space X is complementably universal for all subspaces of c₀ which have the bounded approximation property, then X^* is non-separable (and hence X does not embed into c₀).B.There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X. Theorem B solves a problem that dates from the 1970s.

Original language	English
Pages (from-to)	3395-3408
Number of pages	14
Journal	Journal of Functional Analysis
Volume	257
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2009.07.008
State	Published - 1 Dec 2009

Keywords

Approximation property
Complemented subspaces
Factorization of compact operators
Universal Banach spaces

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10.1016/j.jfa.2009.07.008

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AB - The two main results are: A.If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X* is non-separable (and hence X does not embed into c0).B.There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X. Theorem B solves a problem that dates from the 1970s.

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KW - Complemented subspaces

KW - Factorization of compact operators

KW - Universal Banach spaces

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Complementably universal Banach spaces, II

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Complementably universal Banach spaces, II

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