O'Loughlin, R (2022) Matrix-valued truncated Toeplitz operators: unbounded symbols, kernels and equivalence after extension. Integral Equations and Operator Theory, 94 (1). 5. ISSN 0378-620X
Abstract
This paper studies matrix-valued truncated Toeplitz operators, which are a vectorial generalisation of truncated Toeplitz operators. It is demonstrated that, although there exist matrix-valued truncated Toeplitz operators without a matrix symbol in Lp for any p∈(2,∞], there is a wide class of matrix-valued truncated Toeplitz operators which possess a matrix symbol in Lp for some p∈(2,∞]. In the case when the matrix-valued truncated Toeplitz operator has a symbol in Lp for some p∈(2,∞], an approach is developed which bypasses some of the technical difficulties which arise when dealing with problems concerning matrix-valued truncated Toeplitz operators with unbounded symbols. Using this new approach, two new notable results are obtained. The kernel of the matrix-valued truncated Toeplitz operator is expressed as an isometric image of an S∗-invariant subspace. Also, a Toeplitz operator is constructed which is equivalent after extension to the matrix-valued truncated Toeplitz operator. In a different yet overlapping vein, it is also shown that multidimensional analogues of the truncated Wiener–Hopf operators are unitarily equivalent to certain matrix-valued truncated Toeplitz operators.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Hardy space; Toeplitz operator; Matrix-valued functions; 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: | 28 Jan 2022 15:36 |
Last Modified: | 21 Mar 2023 13:30 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00020-022-02685-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:182735 |