Accessibility navigation


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

[img] Text (Permanent publisher embargo) - Accepted Version
· Restricted to Repository staff only

280kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:81338
Publisher:Royal Swedish Academy of Sciences

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation