Another Characterization of the Invariant Subspace Problem

1995 ◽  
pp. 15-31
Author(s):  
Y. A. Abramovich ◽  
C. D. Aliprantis ◽  
O. Burkinshaw
Keyword(s):  
Invariant Subspace ◽  
Subspace Problem ◽  
Invariant Subspace Problem

scholarly journals Quasireducible operators

2003 ◽  
Vol 2003 (31) ◽  
pp. 1993-2002
Author(s):  
C. S. Kubrusly
Keyword(s):  
Invariant Subspace ◽  
Basic Properties ◽  
Essentially Normal ◽  
Open Questions ◽  
Hyponormal Operators ◽  
Subspace Problem ◽  
Invariant Subspace Problem

We introduce the concept ofquasireducibleoperators. Basic properties and illustrative examples are considered in some detail in order to situate the class of quasireducible operators in its due place. In particular, it is shown thatevery quasinormal operator is quasireducible. The following result links this class with the invariant subspace problem:essentially normal quasireducible operators have a nontrivial invariant subspace, which implies thatquasireducible hyponormal operators have a nontrivial invariant subspace.The paper ends with some open questions on the characterization of the class of all quasireducible operators.

scholarly journals An invariant subspace theorem on subdecomposable operators

2000 ◽  
Vol 61 (1) ◽  
pp. 11-26
Author(s):  
Mingxue Liu
Keyword(s):  
Invariant Subspace ◽  
Additional Condition ◽  
Subspace Theorem ◽  
Subspace Problem ◽  
Invariant Subspace Problem

H. Mohebi and M. Radjabalipour raised a conjecture on the invariant subspace problem in 1994. In this paper, we prove the conjecture under an additional condition, and obtain an invariant subspace theorem on subdecomposable operators.

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