Generalizations of the relation of quasisimilarity for operators
- 주제(키워드) Ampliation quasisimilarity , Hyperinvariant subspace , Quasi-affinity , Quasisimilarity , Quasitriangular operator
- 관리정보기술 faculty
- 등재 SCOPUS
- 발행기관 University of Szeged
- 발행년도 2019
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000172199
- 본문언어 영어
- Published As https://dx.doi.org/10.14232/actasm-019-765-9
초록/요약
In this note we first briefly review the progress on the hyperinvari-ant subspace problem for operators on Hilbert space made possible by the equivalence relation of ampliation quasisimilarity recently introduced in [7]. Then we introduce another equivalence relation, which we call pluquasisimilarity , with bigger equivalence classes than ampliation quasisimilarity but very different in appearance, which preserves the existence of hyperinvariant sub-spaces for operators, and thus may be useful in the future. We also compare these with two other equivalence relations, injection-similarity and complete injection-similarity, introduced long ago by Sz.-Nagy and Foias in [13]. © Bolyai Institute, University of Szeged.
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