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arXiv · 1910.07362

Compact and Limited Operators

Mohammed Bachir·Gonzalo Flores·Sebastián Tapia-García
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Abstract

Let $T:Y\to X$ be a bounded linear operator between two 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.

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Mohammed Bachir, Gonzalo Flores, Sebastián Tapia-García. 2019-10-16. Compact and Limited Operators. https://arxiv.org/abs/1910.07362

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