English

A counterexample of the Fredholm of Toeplitz operator

Functional Analysis 2025-03-12 v1 Complex Variables

Abstract

In this paper we study the essential spectra of the Toeplitz operator on the Hardy space H1H^1. 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.

Keywords

Cite

@article{arxiv.2503.08590,
  title  = {A counterexample of the Fredholm of Toeplitz operator},
  author = {Hua Liu and Xinyang Zhang},
  journal= {arXiv preprint arXiv:2503.08590},
  year   = {2025}
}