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ASYMPTOTIC LIMITS OF OPERATORS SIMILAR TO NORMAL OPERATORS.
- Source :
-
Proceedings of the American Mathematical Society . Nov2015, Vol. 143 Issue 11, p4823-4834. 12p. - Publication Year :
- 2015
-
Abstract
- 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 T-1 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 a 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 143
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 109152118
- Full Text :
- https://doi.org/10.1090/proc/12632