Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2020.03.21
  • Accepted : 2020.09.15
  • Published : 2021.03.31
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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.

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References

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