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Journal Articles Mathematical News / Mathematische Nachrichten Year : 2020

Compact and Limited operators

Abstract

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize the compactness of $T$ in terms of the differentiability of the Lipschitz function defined on $X$ with values in another normed space $Z$. Furthermore, we adapt the technique used in the proof to also characterize finite rank operators in terms of differentiability of a wider class of functions but still with Lipschitz flavour. Moreover, we give an application of the main result on a Banach-Stone-like Theorem. On the other hand, we give an extension of the result of Bourgain and Diestel related to limited operators and strict cosingularity.
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Dates and versions

hal-03039783 , version 1 (04-12-2020)

Identifiers

  • HAL Id : hal-03039783 , version 1

Cite

Mohammed Bachir, Gonzalo Flores, Sebastian Tapia-Garcia. Compact and Limited operators. Mathematical News / Mathematische Nachrichten, In press. ⟨hal-03039783⟩
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