H-Toeplitz Operators on the Bergman Space
Bull. Korean Math. Soc.
Published online November 5, 2020
Anuradha Gupta and Shivam kumar Singh
Department of Mathematics, Delhi college of Arts and Commerce, University of Delhi, Delhi 110023, India, Department of Mathematics, Shaheed Rajguru College of Applied Sciences for Women, University of Delhi, Delhi, India
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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