Bounded toeplitz products on weighted bergman spaces

Karel Stroethoff; Dechao Zheng

Bounded toeplitz products on weighted bergman spaces

Karel Stroethoff, Dechao Zheng

Mathematics

Vanderbilt University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products T_fT_g are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unweighted Bergman space [17]. We will furthermore completely describe when the Toeplitz product T_fT _g is invertible or Fredholm and prove results generalizing those we obtained for the unweighted Bergman space in [18].

Original language	English
Pages (from-to)	277-308
Number of pages	32
Journal	Journal of Operator Theory
Volume	59
Issue number	2
State	Published - Mar 2008

Keywords

Berezin transform
Bounded
Fredholm operators
Invertible
Toeplitz operator
Unit disk
Weighted Bergman spaces

Cite this

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AU - Zheng, Dechao

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AB - We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unweighted Bergman space [17]. We will furthermore completely describe when the Toeplitz product TfT g is invertible or Fredholm and prove results generalizing those we obtained for the unweighted Bergman space in [18].

KW - Berezin transform

KW - Bounded

KW - Fredholm operators

KW - Invertible

KW - Toeplitz operator

KW - Unit disk

KW - Weighted Bergman spaces

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JO - Journal of Operator Theory

JF - Journal of Operator Theory

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ER -

Bounded toeplitz products on weighted bergman spaces

Abstract

Keywords

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