Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(2): 327-347

Online first article November 5, 2020      Printed March 31, 2021

https://doi.org/10.4134/BKMS.b200260

Copyright © The Korean Mathematical Society.

H-Toeplitz operators on the Bergman space

Anuradha Gupta, Shivam Kumar Singh

University of Delhi; University of Delhi

Abstract

As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz operators $B_\phi$ is introduced and studied. Necessary and sufficient conditions under which H-Toeplitz operators become co-isometry and partial isometry are obtained. Some of the invariant subspaces and kernels of H-Toeplitz operators are studied. We have obtained the conditions for the compactness and Fredholmness for H-Toeplitz operators. In particular, it has been shown that a non-zero H-Toeplitz operator can not be a Fredholm operator on the Bergman space. Moreover, we have also discussed the necessary and sufficient conditions for commutativity of H-Toeplitz operators.

Keywords: Toeplitz operator, Hankel operator, H-Toeplitz operator, Bergman space, Berezin transform

MSC numbers: Primary 47B35; Secondary 46E20