This paper demonstrates that the Toeplitz operator with symbol is not Fredholm, contradicting Virtanen's conjecture.
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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Liu et al. (2025) studied this question.
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