Fredholmness of Toeplitz Operators on the Fock Space

Robert Fulsche; Raffael Hagger

doi:10.48550/arXiv.1709.01457

Fredholmness of Toeplitz Operators on the Fock Space

Robert Fulsche^*
, Raffael Hagger

^*Corresponding author for this work

Institute of Analysis

Research output: Contribution to journal › Article › Research › peer review

Abstract

The Fredholm property of Toeplitz operators on the p-Fock spaces Fαp on C ⁿ is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra T _p _, _α on Fαp 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 B ⁿ (Hagger in Integr Equ Oper Theory 89(4):519–556, 2017).

Original language	English
Pages (from-to)	375-403
Number of pages	29
Journal	Complex Analysis and Operator Theory (CAOT)
Volume	13
Issue number	2
E-pub ahead of print	19 May 2018
DOIs	https://doi.org/10.48550/arXiv.1709.01457 https://doi.org/10.1007/s11785-018-0803-8
Publication status	Published - 13 Mar 2019

Keywords

Essential spectrum
Fock spaces
Limit operators
Toeplitz operators

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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Cite this

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title = "Fredholmness of Toeplitz Operators on the Fock Space",

abstract = " The Fredholm property of Toeplitz operators on the p-Fock spaces Fαp on C n is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra T p , α on Fαp 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 B n (Hagger in Integr Equ Oper Theory 89(4):519–556, 2017).",

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