Generalizations of the relation of quasisimilarity for operators

In this note we first briefly review the progress on the hyperinvariant 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,...

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Bibliographic Details
Main Authors: Bercovici Hari
Jung Il Bong
Ko Eungil
Pearcy Carl
Format: Article
Published: 2019
Series:Acta scientiarum mathematicarum 85 No. 3-4
Kulcsszavak:Hiperinvariáns altér, kvázi-hasonlóság
doi:10.14232/actasm-019-765-9

Online Access:http://acta.bibl.u-szeged.hu/66340
Description
Summary:In this note we first briefly review the progress on the hyperinvariant 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 verydifferent in appearance, which preserves the existence of hyperinvariant sub-spaces for operators, and thus may be useful in the future. We also comparethese with two other equivalence relations, injection-similarity and completeinjection-similarity, introduced long ago by Sz.-Nagy and Foias in [13].
Physical Description:681-691
ISSN:2064-8316