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) |