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New York Journal of Mathematics
Volume 31 (2025), 1574-1582

  

Mo Javed and Amit Maji

Invertibility of Bergman Toeplitz operators

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Published: November 25, 2025.
Keywords: Hardy space, Bergman space, Toeplitz operator, Berezin transform.
Subject [2010]: 47B35, 47A05, 30H20.

Abstract
In this paper, we establish the invertibility of the Berezin transform of the symbol as a necessary and sufficient condition for the invertibility of the Toeplitz operator on the Bergman space of the unit disc. More precisely, if φ is a linear combination of a bounded analytic function g and its conjugate, then Tφ is invertible if and only if φ is bounded below.

Acknowledgements

The authors are thankful to the anonymous reviewer for his/her careful reading of the manuscript and for the valuable comments and suggestions.


Author information

Mo Javed
Indian Institute of Technology Roorkee
Department of Mathematics
Roorkee-247 667, Uttarakhand, India

javediitr07@gmail.com

Amit Maji
Indian Institute of Technology Roorkee
Department of Mathematics
Roorkee-247 667, Uttarakhand, India

amit.maji@ma.iitr.ac.in