Kérchy László honlapja

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Cím:Generalized Toeplitz operators associated with operators of regular norm-sequences.
Szerző:K\'erchy, L\'aszl\'o
Forrás:Kubrusly, Carlos (ed.) et al., Semigroups of operators: theory and applications. Proceedings of the 2nd international conference, Rio de Janeiro, Brazil, September 10-14, 2001. New York, NY: Optimization Software Inc., Publications. 119-131 (2002). [ISBN 0-911575-11-1/hbk]
Nyelv:English
Absztrakt:A~(bounded linear) Hilbert space operator $C$ is called $T$-Toeplitz if $T^*CT=r(T)^2C$, where $r(T)$ denotes the spectral radius of~$T$. This paper gives a survey of the author's results on $T$-Toeplitz operators for operators $T$ having a regular norm-sequence. (The~definition of ``an operator having a regular norm-sequence'' is a bit technical and involves Banach limits; suffice it to say that, e.g., any operator $T$ for which $r(T)^{-1}T$ is power bounded has a regular norm-sequence.) \par The~topics covered include the existence of symbol calculi, Arveson's projection mapping, spectral inclusion and other properties of the spectrum, invariant subspaces, and reflexivity. Detailed proofs and additional results can be found in the author's papers [Acta Sci. Math. (Szeged) 68, 373-400 (2002; Zbl 1012.47003)] and ``Reflexive subspaces of generalized Toeplitz operators'' [preprint, per~bibl.].} \RV{Miroslav Engli\v{s} (Praha) 
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