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Cím:Generalized Toeplitz operators
Szerző:K\'erchy, L\'aszl\'o
Forrás:Acta Sci. Math. 68, No.1-2, 373-400 (2002)
Nyelv:English
Absztrakt:A Hilbert space operator $X :H \to H$ is said to be a generalized Toeplitz operator with respect to a given contraction $T $ in $H$ if $T^*XT=X$. A well-known theorem due to Brown and Halmos tells us that classical Toeplitz operators correspond to the particular case when $T$ is the forward shift on the Hardy space $H^2$. The purpose of this line of research, investigated by some authors already, is to study which properties of classical Toeplitz operators depend only on their characteristic relation. Following this spirit, the main novelty of this paper is to deal with the equation $T^*XT=r(T)^2X$, where now $T$ is an arbitrary operator and $r(T)$ stands for its spectral radius. It is shown that a symbolic calculus can be given for a large class of operators $T$ and the spectral properties of this calculus are studied. For further details concerning the results obtained here, we refer the reader to this very interesting paper.} \RV{Pedro J.Pa{\'u}l (Sevilla) 
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