An Exposition on Weak Stability of Operators

2024/08/08 by Kubrusly, C. S.
#47A15 #47A45 #4BA15 #A7B20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2408.04186

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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