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Asymptotic limits of operators similar to normal operators

Gehér, G. P. (2015) Asymptotic limits of operators similar to normal operators. Proceedings of the American Mathematical Society, 143 (11). pp. 4823-4834. ISSN 0002-9939

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To link to this item DOI: 10.1090/proc/12632

Abstract/Summary

Sz.-Nagy’s famous theorem states that a bounded operator T which acts on a complex Hilbert space H is similar to a unitary operator if and only if T is invertible and both T and its inverse are power bounded. There is an equivalent reformulation of that result which considers the self-adjoint iterates of T and uses a Banach limit L. In this paper first we present a generalization of the necessity part in Sz.-Nagy’s result concerning operators that are similar to normal operators. In the second part we provide characterization of all possible strong operator topology limits of the self-adjoint iterates of those contractions which are similar to unitary operators and act on a separable infinite-dimensional Hilbert space. This strengthens Sz.-Nagy’s theorem for contractions.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:81506
Publisher:American Mathematical Society

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