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(The) hyperinvariant subspace problem for quasinilpotent operators
준멱영 작용소의 초불변부분공간문제

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Authors
김형준
Advisor
이우영
Issue Date
2008-08
Publisher
서울대학교 대학원
Keywords
초불변부분공간Hyperinvariant subspaces극벡터extremal vectors준멱영 작용소quasinilpotent 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
URI
http://dcollection.snu.ac.kr:80/jsp/common/DcLoOrgPer.jsp?sItemId=000000041411
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)

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