An Exposition on Weak Stability of Operators
Functional Analysis
2024-08-09 v1
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.
Cite
@article{arxiv.2408.04186,
title = {An Exposition on Weak Stability of Operators},
author = {C. S. Kubrusly},
journal= {arXiv preprint arXiv:2408.04186},
year = {2024}
}