The quotient algebra of compact-by-approximable operators on Banach spaces failing the approximation property

Hans-Olav Tylli, Henrik Johannes Wirzenius

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We initiate a study of structural properties of the quotient algebra K (X)/A(X) of the compact-by-approximable operators on Banach spaces X failing the approximation property. Our main results and examples include the following: (i) there is a linear isomorphic embedding from c(0) into K (Z)/A(Z), where Z belongs to the class of Banach spaces constructed by Willis that have the metric compact approximation property but fail the approximation property, (ii) there is a linear isomorphic embedding from a nonseparable space c(0)(Gamma) into K (Z(FJ))/A(Z(FJ)), where Z(FJ) is a universal compact factorisation space arising from the work of Johnson and Figiel.

Original languageEnglish
JournalJournal of the Australian Mathematical Society
Volume110
Issue number2
Pages (from-to)266-288
Number of pages23
ISSN1446-7887
DOIs
Publication statusPublished - Apr 2021
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics
  • quotient algebra
  • compact-by-approximable operators
  • approximation properties

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