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January 2018 Toeplitz operators on the space of real analytic functions: The Fredholm property
Pawel Domański, Michal Jasiczak
Banach J. Math. Anal. 12(1): 31-67 (January 2018). DOI: 10.1215/17358787-2017-0022

Abstract

We completely characterize those continuous operators on the space of real analytic functions on the real line for which the associated matrix is Toeplitz (that is, we describe Toeplitz operators on this space). We also prove a necessary and sufficient condition for such operators to be Fredholm operators. While the space of real analytic functions is neither Banach space nor has a basis which makes available methods completely different from classical cases of Hardy spaces or Bergman spaces, nevertheless the results themselves show surprisingly strong similarity to the classical Hardy-space theory.

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Pawel Domański. Michal Jasiczak. "Toeplitz operators on the space of real analytic functions: The Fredholm property." Banach J. Math. Anal. 12 (1) 31 - 67, January 2018. https://doi.org/10.1215/17358787-2017-0022

Information

Received: 29 August 2016; Accepted: 7 December 2016; Published: January 2018
First available in Project Euclid: 4 August 2017

zbMATH: 06841264
MathSciNet: MR3745573
Digital Object Identifier: 10.1215/17358787-2017-0022

Subjects:
Primary: 47B35
Secondary: 26A90, 30E20, 30H10, 30H50, 46A13, 46E10, 47A53, 47B38

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 1 • January 2018
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