Journal of Operator Theory

Volume 79, Issue 2, Spring 2018 pp. 327-344.

Coburn--Simonenko theorem and invertibility of Toeplitz operators on the space of real analytic functions

Authors: M. Jasiczak
Author institution: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznan, Poland

Summary: We study Toeplitz operators on the space of real analytic functions. We prove that either such an operator or its adjoint is injective. This is an analog of the classical Coburn--Simonenko theorem. We also show that a Toeplitz operator on the space of real analytic functions is invertible if and only if it is a Fredholm operator of index zero.

DOI: http://dx.doi.org/10.7900/jot.2017mar27.2144
Keywords: Toeplitz operator, space of real analytic functions, Fredholm operator, index, Cauchy transform

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