Quasidiagonality and the hyperinvariant subspace problem |
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Authors: | Sami M Hamid Constantin Onica Carl Pearcy |
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Institution: | (1) Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA;(2) Department of Mathematics, Indiana University, Bloomington, IN 47405, USA;(3) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA |
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Abstract: | In a sequence of recent papers, 11], 13], 9] and 5], the authors (together with H. Bercovici and C. Foias) reduced the
hyperinvariant subspace problem for operators on Hilbert space to the question whether every C
00-(BCP)-contraction that is quasidiagonal and has spectrum the unit disc has a nontrivial hyperinvariant subspace (n.h.s.).
An essential ingredient in this reduction was the introduction of two new equivalence relations, ampliation quasisimilarity
and hyperquasisimilarity, defined below. This note discusses the question whether, by use of these relations, a further reduction
of the hyperinvariant subspace problem to the much-studied class (N + K) (defined below) might be possible. |
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Keywords: | |
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