Toeplitz operators on non-reflexive Fock spaces

2022/02/23 by Fulsche, Robert · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2202.11440

Abstract

We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces F_t^p to the non-reflexive cases p = 1, ∞. 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.

Cited by

• Fredholm operators on abelian phase spaces

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• Berger-Coburn theorem, localized operators, and the Toeplitz algebra
• Weighted theory of Toeplitz operators on the Fock spaces
• Compactness of operators on generalized Fock spaces
• Compactness characterization of operators in the Toeplitz algebra of the Fock space F_α^p
• On Toeplitz operators between Fock spaces