Complementably universal Banach spaces, II

W. B. Johnson*, A. Szankowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)3395-3408
Number of pages14
JournalJournal of Functional Analysis
Volume257
Issue number11
DOIs
StatePublished - 1 Dec 2009

Keywords

  • Approximation property
  • Complemented subspaces
  • Factorization of compact operators
  • Universal Banach spaces

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