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

Cited 0 time in webofscience Cited 0 time in scopus
Kim, Hyoungjoon
Issue Date
초불변부분공간극벡터준멱영 작용소Hyperinvariant subspacesextremal vectorsquasinilpotent 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.
Files in This Item:
There are no files associated with this item.
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses and dissertations (학위논문_수리과학부)
  • mendeley

Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.