scholarly journals On the hyperinvariant subspace problem

2005 ◽  
Vol 219 (1) ◽  
pp. 134-142 ◽  
Author(s):  
Ciprian Foias ◽  
Carl Pearcy
2008 ◽  
Vol 166 (1) ◽  
pp. 285-296
Author(s):  
Sami M. Hamid ◽  
Constantin Onica ◽  
Carl Pearcy

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2563-2566
Author(s):  
Wurichaihu Bai ◽  
Alatancang Chen

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.


2008 ◽  
Vol 60 (4) ◽  
pp. 758-789 ◽  
Author(s):  
H. Bercovici ◽  
C. Foias ◽  
C. Pearcy

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.


2005 ◽  
Vol 222 (1) ◽  
pp. 129-142 ◽  
Author(s):  
C. Foias ◽  
S. Hamid ◽  
C. Onica ◽  
C. Pearcy

2008 ◽  
Vol 60 (4) ◽  
pp. 758 ◽  
Author(s):  
H. Bercovici ◽  
C. Foias ◽  
C. Pearcy

2005 ◽  
Vol 54 (3) ◽  
pp. 743-754 ◽  
Author(s):  
Sami M. Hamid ◽  
Constantin Onica ◽  
Carl Pearcy

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