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### SHERP

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

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Authors
Issue Date
2008-08
Keywords
초불변부분공간; 극벡터; 준멱영 작용소; Hyperinvariant subspaces; extremal vectors; quasinilpotent operators
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://hdl.handle.net/10371/758
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 and dissertations (학위논문_수리과학부)