Generalizations of the relation of quasisimilarity for operators

Bercovici Hari and Jung Il Bong and Ko Eungil and Pearcy Carl: Generalizations of the relation of quasisimilarity for operators. In: Acta scientiarum mathematicarum, (85) 3-4. pp. 681-691. (2019)

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Abstract

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].

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 3-4
ISSN: 2064-8316
Page Range: pp. 681-691
Related URLs: http://acta.bibl.u-szeged.hu/66425/
DOI: 10.14232/actasm-019-765-9
Uncontrolled Keywords: Hiperinvariáns altér, kvázi-hasonlóság
Additional Information: Bibliogr.: p. 690-691.
Date Deposited: 2020. Apr. 23. 14:58
Last Modified: 2021. Mar. 25. 15:34
URI: http://acta.bibl.u-szeged.hu/id/eprint/66340

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