On the Dilation of Truncated Toeplitz Operators

Eungil Ko; Ji Eun Lee

doi:10.1007/s11785-015-0482-7

On the Dilation of Truncated Toeplitz Operators

Eungil Ko, Ji Eun Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

An operator (Formula presented.) is called the dilation of a truncated Toeplitz operator if for two symbols (Formula presented.) and an inner function u, (Formula presented.) for (Formula presented.) where (Formula presented.) denotes the orthogonal projection of (Formula presented.) onto the model space (Formula presented.) and (Formula presented.) In this paper, we study properties of the dilation of truncated Toeplitz operators on (Formula presented.). In particular, we provide conditions for the dilation of truncated Toeplitz operators to be normal. As some applications, we give several examples of such operators.

Original language	English
Pages (from-to)	815-833
Number of pages	19
Journal	Complex Analysis and Operator Theory
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s11785-015-0482-7
State	Published - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Basel.

Keywords

Dilation of truncated Toeplitz operator
Hyponormal operator
Normal operator
Selfadjoint operator

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10.1007/s11785-015-0482-7

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AB - An operator (Formula presented.) is called the dilation of a truncated Toeplitz operator if for two symbols (Formula presented.) and an inner function u, (Formula presented.) for (Formula presented.) where (Formula presented.) denotes the orthogonal projection of (Formula presented.) onto the model space (Formula presented.) and (Formula presented.) In this paper, we study properties of the dilation of truncated Toeplitz operators on (Formula presented.). In particular, we provide conditions for the dilation of truncated Toeplitz operators to be normal. As some applications, we give several examples of such operators.

KW - Dilation of truncated Toeplitz operator

KW - Hyponormal operator

KW - Normal operator

KW - Selfadjoint operator

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On the Dilation of Truncated Toeplitz Operators

Abstract

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Keywords

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