Sarason Toeplitz product problem for a class of Fock spaces

2020/04/08 by Hélène Bommier-Hato, Bommier-Hato, Helene, El Hassan Youssfi +3 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2004.04094

openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sarason Toeplitz product problem asks when the operator TuTv is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.

Cited by

• Compactness of products of block Hankel and Toeplitz operators
• Fixed points of the Berezin transform on Fock-type spaces

Related

• On products of some Toeplitz operators on polyanalytic Fock spaces
• Boundedness and Compactness of products of Toeplitz operators on the Bergman Space
• Products of Toeplitz operators on the Fock space
• Products of Toeplitz and Hankel Operators on Fock-Sobolev Spaces
• A Product Expansion for Toeplitz Operators on the Fock Space