Hyperinvariant subspaces for a class of quasinilpotent operators
- 주제(키워드) invariant subspace , hyperinvariant subsace , quasinilpotent operator , centered operator , weakly centered operator
- 주제(기타) Mathematics
- 설명문(일반) [Jung, Il Bong] Kyungpook Natl Univ, Dept Math, Daegu 41566, South Korea; [Ko, Eungil] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea; [Pearcy, Carl] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000155690
- 본문언어 영어
- Published As http://dx.doi.org/10.4064/sm171209-18-1
초록/요약
Quasinilpotent operators on Hilbert space are very little understood. Except for the classification, up to similarity, as parts of quasinilpotent backward weighted shifts of infinite multiplicity (Foias and Pearcy, 1974), and the recently introduced technique of extremal vectors (see the references), there are few known structure theorems or theorems proving the existence of invariant or hyperinvariant subspaces for such operators. In this paper we use a structure theorem for the class of weakly centered operators (Paulsen et al., 1995) to obtain a structure theorem for a certain subclass of quasinilpotent operators that immediately yields the existence of hyperinvariant subspaces for such operators.
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