Toeplitz operators on non-reflexive Fock spaces

TL;DR

This paper extends key properties of Toeplitz operators from reflexive to non-reflexive Fock spaces, including compactness, Fredholmness, and algebra representations, enhancing the theoretical framework of operator analysis.

Contribution

It generalizes fundamental results on Toeplitz operators to non-reflexive Fock spaces, providing new characterizations and improved correspondence theory results.

Findings

Characterization of compactness and Fredholm property for non-reflexive cases

Representation of the Toeplitz algebra in non-reflexive Fock spaces

Enhanced correspondence theory and Berger-Coburn estimates

Abstract

We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces $F_t^p$ to the non-reflexive cases $p = 1, \infty$. Among these results are the characterization of compactness and the Fredholm property of such operators, a well-known representation of the Toeplitz algebra, a characterization of the essential centre of the Toeplitz algebra. Further, we improve several results related to correspondence theory, e.g. we improve previous results on the correspondence of algebras and we give a correspondence theoretic version of the well-known Berger-Coburn estimates.