A Wiener algebra for Fock space operators

2023/11/20 by Fulsche, Robert
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2311.11859

Abstract

We introduce an algebra \mathcal W_t of linear operators that act continuously on each of the Fock spaces F_t^p, 1 ≤ p ≤ ∞, and contains all Toeplitz operators with bounded symbols. We show that compactness, the spectrum, essential spectrum and the Fredholm index of an element of \mathcal W_t, realized as an operator on F_t^p, are independent of the value of p.

Related

• Compactness characterization of operators in the Toeplitz algebra of the Fock space F_α^p
• Toeplitz algebra on the Fock space
• Toeplitz operators on non-reflexive Fock spaces
• Berger-Coburn theorem, localized operators, and the Toeplitz algebra
• Essential Commutants and Characterizations of the Toeplitz Algebra