Asymptotic behaviours and generalized Toeplitz operators
type: Item
instance of: scholarly article
title: Asymptotic behaviours and generalized Toeplitz operators
zbMATH Open document ID: 1151.47037
author: Laurian Suciu
author: N. Suciu
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-11-06T00:00:00Z
review text: The paper deals with certain generalized Toeplitz operators associated to operators \(T\) on a Hilbert space \(H\). In particular, when considering bounded linear operators \(T \in B(H)\) for which the sequence \({(\| T^n h\| )}_{n\in {\mathbb N}}\) converges for every \(h \in H\), the authors present conditions for \(T\) to be orthogonally mean ergodic. Moreover, the asymptotic limit \(S_T\) of such a \(T\) is written in terms of the ergodic projections of \(T\) and \(T^\ast\), and the unitary part for \(T\) in \(H\) is obtained. Some results of [\textit{R. G. Douglas}, Acta Sci. Math. 30, 19--32 (1969; Zbl 0177.19204)] concerning the generalized Toeplitz operators for contractions are extended. To this end, the authors apply the theory to operators of the class \(C_\rho\) (\(\rho > 0\)) in the sense of \textit{B. Sz.-Nagy} and \textit{C. Foias} [``Harmonic analysis of operators on Hilbert spaces'', Budapest: Akadémiai Kiadó, Amsterdam-London: North-Holland (1970; Zbl 0201.45003)].
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 5362153
zbMATH Keywords: generalized Toeplitz operator
zbMATH Keywords: orthogonally mean ergodic operator
zbMATH Keywords: \(A\)-contraction
zbMATH Keywords: \(\rho\)-contraction
zbMATH Keywords: invariant subspace
zbMATH Keywords: orthogonal projection
reviewed by: L. P. Castro
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.08.028
OpenAlex ID: W1977060699
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DOI: 10.1016/J.JMAA.2008.08.028
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description: scientific article; zbMATH DE number 5362153