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

DC Field Value Language
dc.contributor.advisor이우영-
dc.contributor.author김형준-
dc.date.accessioned2008-08-
dc.date.available2008-08-01-
dc.date.copyright2008-
dc.date.issued2008-08-
dc.identifier.other000000041411-
dc.identifier.urihttp://dcollection.snu.ac.kr:80/jsp/common/DcLoOrgPer.jsp?sItemId=000000041411-
dc.descriptionThesis(doctors)--서울대학교 대학원 :수리과학부,2008.8.-
dc.description.abstractThis 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.-
dc.format.extentii, 72 leaves.-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subject초불변부분공간-
dc.subjectHyperinvariant subspaces-
dc.subject극벡터-
dc.subjectextremal vectors-
dc.subject준멱영 작용소-
dc.subjectquasinilpotent operators-
dc.title(The) hyperinvariant subspace problem for quasinilpotent operators-
dc.title.alternative준멱영 작용소의 초불변부분공간문제-
dc.typeThesis-
dc.contributor.AlternativeAuthorKim, Hyoungjoon-
dc.contributor.department수리과학부-
dc.description.degreeThesis(doctors) ---
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