On the hyperinvariant subspace problem

Ciprian Foias; Carl Pearcy

doi:10.1016/j.jfa.2004.04.003

On the hyperinvariant subspace problem

Journal of Functional Analysis ◽

10.1016/j.jfa.2004.04.003 ◽

2005 ◽

Vol 219 (1) ◽

pp. 134-142 ◽

Cited By ~ 3

Author(s):

Ciprian Foias ◽

Carl Pearcy

Keyword(s):

Hyperinvariant Subspace ◽

Subspace Problem

Download Full-text

Quasidiagonality and the hyperinvariant subspace problem

Israel Journal of Mathematics ◽

10.1007/s11856-008-1031-0 ◽

2008 ◽

Vol 166 (1) ◽

pp. 285-296

Author(s):

Sami M. Hamid ◽

Constantin Onica ◽

Carl Pearcy

Keyword(s):

Hyperinvariant Subspace ◽

Subspace Problem

Download Full-text

Quasi-nilpotent Operators and Hyperinvariant Subspace Problem

Bulletin of the Iranian Mathematical Society ◽

10.1007/s41980-018-0128-4 ◽

2018 ◽

Vol 45 (1) ◽

pp. 233-237

Author(s):

Mohammad B. Asadi ◽

Rasoul Eskandari

Keyword(s):

Hyperinvariant Subspace ◽

Nilpotent Operators ◽

Subspace Problem

Download Full-text

On local spectral properties of Hamilton operators

Filomat ◽

10.2298/fil1807563b ◽

2018 ◽

Vol 32 (7) ◽

pp. 2563-2566

Author(s):

Wurichaihu Bai ◽

Alatancang Chen

Keyword(s):

Spectral Properties ◽

Hyperinvariant Subspace ◽

Weyl Type Theorems ◽

Subspace Problem ◽

Adjoint Operators

This paper deals with local spectral properties of Hamilton type operators. The strongly decomposability, Weyl type theorems and hyperinvariant subspace problem of them and the similar properties with their adjoint operators are studied. As corollaries, some local spectral properties of Hamilton operators are obtained.

Download Full-text

On the Hyperinvariant Subspace Problem. IV

Canadian Journal of Mathematics ◽

10.4153/cjm-2008-034-2 ◽

2008 ◽

Vol 60 (4) ◽

pp. 758-789 ◽

Cited By ~ 1

Author(s):

H. Bercovici ◽

C. Foias ◽

C. Pearcy

Keyword(s):

Hilbert Space ◽

Compact Operator ◽

Essential Spectrum ◽

Complete Lattice ◽

Unit Disc ◽

Diagonal Operator ◽

Hyperinvariant Subspace ◽

Infinite Dimensional ◽

Infinite Dimensional Hilbert Space ◽

Subspace Problem

AbstractThis paper is a continuation of three recent articles concerning the structure of hyperinvariant subspace lattices of operators on a (separable, infinite dimensional) Hilbert space . We show herein, in particular, that there exists a “universal” fixed block-diagonal operator B on such that if ε > 0 is given and T is an arbitrary nonalgebraic operator on , then there exists a compact operator K of norm less than ε such that (i) Hlat(T) is isomorphic as a complete lattice to Hlat(B + K) and (ii) B + K is a quasidiagonal, C00, (BCP)-operator with spectrum and left essential spectrum the unit disc. In the last four sections of the paper, we investigate the possible structures of the hyperlattice of an arbitrary algebraic operator. Contrary to existing conjectures, Hlat(T) need not be generated by the ranges and kernels of the powers of T in the nilpotent case. In fact, this lattice can be infinite.

Download Full-text