September 29, 2025Open Access

A counterexample of the Fredholm of Toeplitz operator

Key Points

The study reveals a counterexample that shows the Toeplitz operator is not Fredholm.
Counterexample challenges a prior conjecture made by J.A. Virtanen in 2006 about the Toeplitz operator.
Research focuses on essential spectra within the framework of Hardy spaces.
Findings may reshape understanding of Toeplitz operators and their spectrum properties.

Abstract

In this paper we study the essential spectra of the Toeplitz operator on the Hardy space H¹. We give a counterexample to show that the Toeplitz operator with symbol is not Fredholm, which gives a counterexample to the conjecture by J. A. Virtanen J A in 2006.

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Cite This Study

Liu et al. (Tue,) studied this question.

synapsesocial.com/papers/68da58d1c1728099cfd10b2e https://doi.org/https://doi.org/10.48550/arxiv.2503.08590

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