On properties of the operator equation TT* = T plus T*
- 주제(키워드) Operator equations , spectrum , single valued extension property
- 주제(기타) Mathematics, Applied; Mathematics
- 설명문(일반) [An, Il Ju] Ewha Womans Univ, Inst Math Sci, Seoul 03760, South Korea; [Ko, Eungil] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 UNIV NIS, FAC SCI MATH
- 발행년도 2018
- URI http://www.dcollection.net/handler/ewha/000000159708
- 본문언어 영어
- Published As http://dx.doi.org/10.2298/FIL1806247A
초록/요약
In this paper, we study properties of the operator equation TT* = T + T* which T. T. West observed in [12]. We first investigate the structure of solutions T is an element of B(H) of such equation. Moreover, we prove that if T is a polynomial root of solutions of that operator equation, then the spectral mapping theorem holds for Weyl and essential approximate point spectra of T and f (T) satisfies a-Weyl's theorem for f 2 H(sigma(T)), where H(sigma(T)) is the space of functions analytic in an open neighborhood of sigma(T).
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