TY - JOUR
T1 - Generalizations of the relation of quasisimilarity for operators
AU - Bercovici, H.
AU - Jung, I. B.
AU - Ko, E.
AU - Pearcy, C.
N1 - Funding Information:
Received February 23, 2019 and in final form March 28, 2019. AMS Subject Classification (2010): 47A15; 47A65. Key words and phrases: hyperinvariant subspace, quasisimilarity, ampliation quasisimilarity, quasi-affinity, quasitriangular operator. ∗Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2018R1A2B6003660). †Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).
Publisher Copyright:
© Bolyai Institute, University of Szeged.
PY - 2019
Y1 - 2019
N2 - 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].
AB - 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].
KW - Ampliation quasisimilarity
KW - Hyperinvariant subspace
KW - Quasi-affinity
KW - Quasisimilarity
KW - Quasitriangular operator
UR - http://www.scopus.com/inward/record.url?scp=85077875149&partnerID=8YFLogxK
U2 - 10.14232/actasm-019-765-9
DO - 10.14232/actasm-019-765-9
M3 - Article
AN - SCOPUS:85077875149
SN - 0001-6969
VL - 85
SP - 681
EP - 691
JO - Acta Scientiarum Mathematicarum
JF - Acta Scientiarum Mathematicarum
IS - 3-4
ER -