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

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Kim, Hyoungjoon
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초불변부분공간; 극벡터; 준멱영 작용소; Hyperinvariant subspaces; extremal vectors; quasinilpotent operators
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.
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses and dissertations (학위논문_수리과학부)
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