Toeplitz operators in Bargmann spaces
type: Item
instance of: scholarly article
title: Toeplitz operators in Bargmann spaces
zbMATH Open document ID: 0644.47028
DOI: 10.1007/BF01272117
author: Henri-François Gautrin
published in: Integral Equations and Operator Theory
publication date: 1988-01-01T00:00:00Z
review text: The Bargmann space is the space of the entire functions in \({\mathbb{C}}^ n,\) for which \(\int | f(z)|\) \(2e-| z|\) \(2dzd\bar z<\infty\). The author proves that the bounded Toeplitz operators in a Bargmann space are dense in the set of bounded operators with respect to the uniform topology. In the last part the author generalizes the notion of Toeplitz operator and shows that all bounded operators are generalized Toeplitz operators. The results generalize some theorems of V. Guillemin, C. A. Berger and L. Coburn.
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 4050345
zbMATH Keywords: Bargmann space
zbMATH Keywords: bounded Toeplitz operators
zbMATH Keywords: Toeplitz operator
reviewed by: Yu V. Egorov
MaRDI profile type: Publication
cites work: Q3943453
cites work: On a Hilbert space of analytic functions and an associated integral transform part I
cites work: On a Hilbert Space of Analytie Functions and an Associated Integral Transform. Part II. A Family of Related Function Spaces Application to Distribution Theory
cites work: Toeplitz operators and quantum mechanics
cites work: A symbol calculus for Toeplitz operators
cites work: Q5569655
cites work: Toeplitz operators in \(n\)-dimensions
cites work: Q4167181
cites work: Équations différentielles d'ordre infini
cites work: Sur les fonctionnelles analytiques et la transformation de Fourier-Borel
cites work: Q4066086
description: scientific article; zbMATH DE number 4050345