On an analogue of a theorem by Astala and Tylli

Alexei Karlovich, Eugene Shargorodsky

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1 Citation (Scopus)


Let ‖ A‖ e be the essential norm of an operator A and ‖ A‖ m be the infimum of the norms of restrictions of A to the subspaces of finite codimension. We show that if ‖ A‖ e< M‖ A‖ m holds for every bounded noncompact operator A from a Banach space X to every Banach space Y, then the space X has the dual compact approximation property. This is an analogue of a result by Astala and Tylli (J Funct Anal 70(2):388–401, 1987) concerning the Hausdorff measure of noncompactness and the bounded compact approximation property.

Original languageEnglish
Pages (from-to)73-77
Number of pages5
JournalArchiv der Mathematik
Issue number1
Publication statusPublished - Jan 2022


  • Bounded compact approximation property
  • Dual compact approximation property
  • Essential norm
  • Measures of noncompactness


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