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) |

Letöltés: | | Zentralblatt |