Toeplitz operators with piecewise continuous symbols on the Hardy space H 1

Miihkinen, S. and Virtanen, J. (2019) Toeplitz operators with piecewise continuous symbols on the Hardy space H 1. Arkiv för Matematik, 57 (2). pp. 429-435. ISSN 1871-2487

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To link to this item DOI: 10.4310/ARKIV.2019.v57.n2.a9

Abstract/Summary

The geometric descriptions of the (essential) spectra of Toeplitz operators with piecewise continuous symbols are among the most beautiful results about Toeplitz operators on Hardy spaces $H^p$ with $1<p<\infty$. In the Hardy space $H^1$, the essential spectra of Toeplitz operators are known for continuous symbols and symbols in the Douglas algebra $C+H^\infty$. It is natural to ask whether the theory for piecewise continuous symbols can also be extended to $H^1$. We answer this question in negative and show in particular that the Toeplitz operator is never bounded on $H^1$ if its symbol has a jump discontinuity.

Item Type: Article Yes Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 81338 Royal Swedish Academy of Sciences

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