Câmara, MC and Partington, JR orcid.org/0000-0002-6738-3216 (2016) Spectral properties of truncated Toeplitz operators by equivalence after extension. Journal of Mathematical Analysis and Applications, 433 (2). pp. 762-784. ISSN 0022-247X
Abstract
We study truncated Toeplitz operators in model spaces View the MathML source for 1<p<∞, with essentially bounded symbols in a class including the algebra View the MathML source, as well as sums of analytic and anti-analytic functions satisfying a θ -separation condition, using their equivalence after extension to Toeplitz operators with 2×2 matrix symbols. We establish Fredholmness and invertibility criteria for truncated Toeplitz operators with θ -separated symbols and, in particular, we identify a class of operators for which semi-Fredholmness is equivalent to invertibility. For symbols in View the MathML source, we extend to all p∈(1,∞) the spectral mapping theorem for the essential spectrum. Stronger results are obtained in the case of operators with rational symbols, or if the underlying model space is finite-dimensional.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Elsevier. This is an author produced version of a paper published in Journal of Mathematical Analysis and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Truncated Toeplitz operator; Toeplitz operator; Equivalence by extension; Model space |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Aug 2015 10:35 |
Last Modified: | 16 May 2019 18:42 |
Published Version: | http://dx.doi.org/10.1016/j.jmaa.2015.08.019 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jmaa.2015.08.019 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:88873 |