On the hyperinvariant subspace problem. II Academic Article

abstract

• Recently in [6] the question of whether every non-scalar operator on a complex Hilbert space H of dimension N0 has a nontrivial hyperinvariant subspace was reduced to a special case; namely, the question whether every (BCP)-operator in C00 whose left essential spectrum is equal to some annulus centered at the origin has a nontrivial hyperinvariant subspace. In this note, we make additional contributions to this circle of ideas by showing that every (BCP)-operator in C00 is ampliation quasisimilar to a quasidiagonal (BCP)-operator in C00. Moreover, we show that there exists a fixed block diagonal (BCP)-operator Bu with the property that if every compact perturbation Bu + K of B u in (BCP) and C00 with K < has a nontrivial hyperinvariant subspace, then every nonscalar operator on H has a nontrivial hyperinvariant subspace. Indiana University Mathematics Journal ,.

authors

• Onica, Constantin

published proceedings

• INDIANA UNIVERSITY MATHEMATICS JOURNAL

author list (cited authors)

• Hamid, S., Onica, C., & Pearcy, C.

citation count

• 6

complete list of authors

• Hamid, S||Onica, C||Pearcy, C

publication date

• August 2005

publisher

• Indiana University  Publisher

published in

• INDIANA UNIVERSITY MATHEMATICS JOURNAL  Journal

keywords

• Hyperinvariant Subspace
• Quasidiagonal
• Quasisimilar

Digital Object Identifier (DOI)

• 10.1512/iumj.2005.54.2639

start page

• 743

end page

• 754

volume

• 54

issue

• 3

URL

• http://dx.doi.org/10.1512/iumj.2005.54.2639