Remark on the dilation of truncated Toeplitz operators
- 주제(키워드) Dilation of truncated Toeplitz operator , isometry , self-adjoint , Square roots of an isometry and a self-adjoint operator
- 주제(기타) Mathematics, Applied; Mathematics
- 설명문(일반) [Ko, Eungil] Ewha Womans Univ, Dept Math, Seoul, South Korea; [Lee, Ji Eun] Sejong Univ, Dept Math & Stat, Seoul 05006, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 UNIV NIS, FAC SCI MATH
- 발행년도 2023
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000211489
- 본문언어 영어
- Published As https://doi.org/10.2298/FIL2326765K
초록/요약
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).
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