Compact and limited operators

Mohammed Bachir, Gonzalo Flores and Sebastián Tapia‐García

Mathematische Nachrichten, 2021, vol. 294, issue 6, 1085-1098

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.

Date: 2021
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https://doi.org/10.1002/mana.201900329

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