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On the hyperinvariant subspace problem III
- Source :
-
Journal of Functional Analysis . May2005, Vol. 222 Issue 1, p129-142. 14p. - Publication Year :
- 2005
-
Abstract
- Abstract: In two recent papers (Foias and Pearcy, J. Funct. Anal., in press, Hamid et al., Indiana Univ. Math. J., to appear), the authors reduced the hyperinvariant subspace problem for operators on Hilbert space to the question whether every -BCP-operator that is quasidiagonal and has spectrum the unit disc has a nontrivial hyperinvariant subspace (n.h.s.). In this note, we continue this study by showing, with the help of a new equivalence relation, that every operator whose spectrum is uncountable, as well as every nonalgebraic operator with finite spectrum, has a hyperlattice (i.e., lattice of hyperinvariant subspaces) that is isomorphic to the hyperlattice of a , quasidiagonal, (BCP)-operator whose spectrum is the closed unit disc. [Copyright &y& Elsevier]
- Subjects :
- *HILBERT space
*BANACH spaces
*SET theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 222
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 16770080
- Full Text :
- https://doi.org/10.1016/j.jfa.2004.07.002