ON BACKWARD ALUTHGE ITERATES OF COMPLEX SYMMETRIC OPERATORS
- 주제(키워드) Backward Aluthge iterate , complex symmetric operator , second keyword , nilpotent operator , hyperinvariant subspace , Weyl's type theorem
- 주제(기타) Mathematics
- 설명문(일반) [Ko, Eungil] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea; [Lee, Ji Eun] Sejong Univ, Dept Math & Stat, Seoul 05006, South Korea; [Lee, Mee-Jung] Ewha Womans Univ, Inst Math Sci, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 gold
- 발행기관 ELEMENT
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000193063
- 본문언어 영어
- Published As https://doi.org/10.7153/mia-2022-25-23
초록/요약
For a nonnegative integer k, an operator T is an element of L(H) is called a backward Aluthge iterate of a complex symmetric operator of order k if the kth Aluthge iterate (T) over tilde ((k)) of T is a complex symmetric operator, denoted by T is an element of BAIC(k). In this paper, we study several properties of the backward Aluthge iterate of a complex symmetric operator. We show that every nilpotent operator of order k + 2 belongs to BAIC(k). Moreover. we prove that if T belongs to BAIC(k), then T has the property (beta) if and only if T is decomposable. Finally, we show that. under some conditions. operators in BAIC(k) have nontrivial hyperinvariant subspaces and we consider Weyl type theorems for such operators.
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