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Remark on the dilation of truncated Toeplitz operators
- Title
- Remark on the dilation of truncated Toeplitz operators
- Authors
- Ko, Eungil; Lee, Ji Eun
- Ewha Authors
- 고응일
- SCOPUS Author ID
- 고응일
- Issue Date
- 2023
- Journal Title
- FILOMAT
- ISSN
- 0354-5180
- Citation
- FILOMAT vol. 37, no. 26, pp. 8765 - 8776
- Keywords
- Dilation of truncated Toeplitz operator; isometry; self-adjoint; Square roots of an isometry and a self-adjoint operator
- Publisher
- UNIV NIS, FAC SCI MATH
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- An operator Su & phi;,& psi; on L2 is called the dilation of a truncated Toeplitz operator if for two symbols & phi;, & psi; & ISIN; L & INFIN; and an inner function u, Su & phi;,& psi; f = & phi;Pu f +& psi;Quf holds for f & ISIN; L2 where Pu is the orthogonal projection of L2 onto Ku2 and Qu = I - Pu. In this paper, we study the squares of the dilation of truncated Toeplitz operators and the relation among its component operators. In particular, we provide characterizations for the square of the dilation of truncated Toeplitz operators Su & phi;,& psi; to be an isometry and a self-adjoint operator, respectively. As applications of the results, we find the cases where (Su & phi;,& psi;)2 is self-adjoint (resp., isometric) but Su & phi;,& psi; is not self-adjoint (resp., isometric).
- DOI
- 10.2298/FIL2326765K
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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