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http://dx.doi.org/10.4134/BKMS.b200260

H-TOEPLITZ OPERATORS ON THE BERGMAN SPACE  

Gupta, Anuradha (Department of Mathematics Delhi college of Arts and Commerce University of Delhi)
Singh, Shivam Kumar (Department of Mathematics Shaheed Rajguru College of Applied Sciences for Women University of Delhi)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 327-347 More about this Journal
Abstract
As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz operators B�� 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;
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