An Exposition on Weak Stability of Operators

C. S. Kubrusly

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arXiv · 2408.04186

An Exposition on Weak Stability of Operators

C. S. Kubrusly

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Abstract

This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability, containing a few new results and some unanswered questions. It also gives an updated review of the literature on the weak stability of operators over the past sixty years, including present-day research trends. It is verified that the majority of the weak stability literature is concentrated on Hilbert-space operators. We discuss why this preference occurs and also why the weak stability of unitary operators is central to the Hilbert-space stability problem.

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C. S. Kubrusly. 2024-08-08. An Exposition on Weak Stability of Operators. https://arxiv.org/abs/2408.04186

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