On the hyperinvariant subspace problem III Academic Article

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 C00 - (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 C00, quasidiagonal, (BCP)-operator whose spectrum is the closed unit disc. Elsevier Inc. All rights reserved.

authors

• Onica, Constantin

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

author list (cited authors)

• Foias, C., Hamid, S., Onica, C., & Pearcy, C.

citation count

• 3

complete list of authors

• Foias, C||Hamid, S||Onica, C||Pearcy, C

publication date

• January 2005

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Hyperinvariant Subspace
• Hyperlattice
• Quasisimilar

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2004.07.002

start page

• 129

end page

• 142

volume

• 222

issue

• 1

URL

• http://dx.doi.org/10.1016/j.jfa.2004.07.002