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Compact and limited operators

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  • Mohammed Bachir
  • Gonzalo Flores
  • Sebastián Tapia‐García

Abstract

Let T:Y→X be a bounded linear operator between two real normed spaces. We characterize compactness of T in terms of differentiability of the Lipschitz functions defined on X with values in another normed space Z. Furthermore, using a similar technique we can also characterize finite rank operators in terms of differentiability of a wider class of functions but still with Lipschitz flavour. As an application we obtain a Banach–Stone‐like theorem. On the other hand, we give an extension of a result of Bourgain and Diestel related to limited operators and cosingularity.

Suggested Citation

  • Mohammed Bachir & Gonzalo Flores & Sebastián Tapia‐García, 2021. "Compact and limited operators," Mathematische Nachrichten, Wiley Blackwell, vol. 294(6), pages 1085-1098, June.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:6:p:1085-1098
    DOI: 10.1002/mana.201900329
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