Berger-Coburn theorem, localized operators, and the Toeplitz algebra

2019/05/29 by Bauer, Wolfram, Fulsche, Robert
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47B35 #Secondary 47L80

paper · doi:10.48550/arxiv.1905.12246

Abstract

We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of p-Fock spaces (1≤ p ≤ ∞). We present an overview of recent results by various authors on the compactness characterization via the Berezin transform for certain operators acting on the Fock space. Based on these results we present three new characterizations of the Toeplitz C^* algebra generated by Toeplitz operators with bounded symbols.

Related

• Compactness characterization of operators in the Toeplitz algebra of the Fock space F_α^p
• Toeplitz operators on the Fock space via the Fourier transform
• Toeplitz operators on non-reflexive Fock spaces
• Compactness of operators on generalized Fock spaces
• Boundedness and compactness of operators on the Fock space