Abstract We discuss an extension of Toeplitz quantization based on polyanalytic functions. derive isomorphism theorem for operators between weighted Sobolev-Fock spaces functions, which are images modulation under Bargmann transforms. This generalizes well-known results from the analytic setting. Finally, we asymptotic symbol calculus and present expansion complex Weyl in terms operators.

In this article, we investigate, a certain localised version of the single-valued extension property for a bounded linear operator on a Banach space. We show that this condition behaves canonically under the Riesz functional calculus, and derive a number of characterisations in terms of kernel-type and range-type spaces for the operator and its adjoint. The theory is exemplified in the case of ...

Using the functional calculus for a normal operator, we provide a result for generalized Toeplitz operators, analogous to the theorem of Axler and Shields on harmonic extensions of the disc algebra. Besides that result, we prove that if T is an injective subnormal weighted shift, then any two nontrivial subspaces invariant under T cannot be orthogonal to each other. Then we show that the C∗-alg...

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space H Cn of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap...

Abstract In this survey we report about recent work on weighted Banach spaces of analytic functions the unit disc and whole complex plane defined with sup-norms operators between them. Results solid hull core these distance formulas are reviewed. Differentiation integration operators, Cesàro Volterra composition superposition Toeplitz analyzed. Boundedness, compactness, spectrum, hypercyclicity...