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(The) hyperinvariant subspace problem for quasinilpotent operators : 준멱영 작용소의 초불변부분공간문제
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- Authors
- Advisor
- 이우영
- Issue Date
- 2008-08
- Publisher
- 서울대학교 대학원
- Keywords
- 초불변부분공간 ; Hyperinvariant subspaces ; 극벡터 ; extremal vectors ; 준멱영 작용소 ; quasinilpotent operators
- Description
- Thesis(doctors)--서울대학교 대학원 :수리과학부,2008.8.
- Abstract
- This dissertation concerns the yperinvariant subspace problem for quasinilpotent operators: Does every quasinilpotent operator on a complex infinite-dimensional separable Hilbert space have a nontrivial hyperinvariant subspace\,? We consider this problem by using the extremal vector technique and the model theory of quasinilpotent operators. Firstly, we focus on quasinilpotent operators in the class $(\mathcal{CRQ})$ with some constraints and then get partial solutions to the hyperinvariant subspace problem for quasinilpotent operators. Secondly, we introduce the notion of `stability' for extremal vectors and then prove that quasinilpotent operators with some stability conditions have nontrivial hyperinvariant subspaces. Finally, we also introduce the notion of `$c$-eigenvectors' and put it into the model theory of quasinilpotent operators to make improvements of the known results on the hyperinvariant subspace problem.
- Language
- English
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