H-Toeplitz operators on the Bergman space
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 327-347
Published online November 5, 2020
Printed March 31, 2021
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
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