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Complex Analysis and Operator Theory

, Volume 13, Issue 2, pp 375–403 | Cite as

Fredholmness of Toeplitz Operators on the Fock Space

  • Robert FulscheEmail author
  • Raffael Hagger
Article

Abstract

The Fredholm property of Toeplitz operators on the p-Fock spaces \(F_\alpha ^p\) on \(\mathbb {C}^n\) is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra \(\mathcal {T}_{p,\alpha }\) on \(F_\alpha ^p\) in terms of the invertibility of limit operators is derived. This paper is based on previous work, which establishes corresponding results on the unit balls \(\mathbb {B}^n\) (Hagger in Integr Equ Oper Theory 89(4):519–556, 2017).

Keywords

Toeplitz operators Fock spaces Essential spectrum Limit operators 

Mathematics Subject Classification

Primary 47B35 Secondary 47L80 47A53 47A10 

Notes

Acknowledgements

We would like to thank Wolfram Bauer for his continuous support and the anonymous referees for their valuable suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für AnalysisLeibniz Universität HannoverHannoverGermany

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