If ϕ is an analytic self-mapping of the unit disc D and if is the Hardy-Hilbert space on D, the composition operator on is defined by . In this article, we consider which Toeplitz operators satisfy
We study Toeplitz operators with radial symbols in weighted Bergman spaces , 1 < p < ∞, on the disc. Using a decomposition of into finite-dimensional subspaces the operator can be considered as a coefficient multiplier. This leads to new results on boundedness of and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of for a satisfying an assumption on the positivity of certain indefinite...
Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples of this new...
In this survey article we describe how the recent work in quantization in multi-variable complex geometry (domains of holomorphy, symmetric domains, tube domains, etc.) leads to interesting results and problems in C*-algebras which can be viewed as examples of the "non-commutative geometry" in the sense of A. Connes. At the same time, one obtains new functional calculi (of pseudodifferential type) with possible applications to partial differential equations and group representations.
Dans cet article nous donnons une formule pour les coefficients de l’inverse des matrices de Toeplitz respectivement de symboles (cas singulier) et (cas régulier) où est une fonction appartenant à une classe de fonctions holomorphes sur un disque ouvert contenant le tore et sans zéro sur . Un cas particulier défini par où et sont des polynômes sans zéro sur est traité. Dans le cas où le symbole est singulier, cette formule présente l’intérêt d’avoir un second ordre. Dans tous les...