Shorter Notes: An Invariant Subspace Theorem

1972 ◽  
Vol 32 (1) ◽  
pp. 331 ◽  
Author(s):  
Mary R. Embry
Keyword(s):  
Invariant Subspace ◽  
Subspace Theorem

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.

A version of the Lomonosov invariant subspace theorem for real Banach spaces

2005 ◽  
Vol 54 (1) ◽  
pp. 257-262 ◽  
Author(s):  
Gleb Sirotkin
Keyword(s):  
Invariant Subspace ◽  
Banach Spaces ◽  
Subspace Theorem

scholarly journals The spectrum of orthogonal sums of subnormal pairs

1988 ◽  
Vol 30 (1) ◽  
pp. 11-15 ◽  
Author(s):  
K. Rudol
Keyword(s):  
Invariant Subspace ◽  
Spectral Theory ◽  
Existence And Uniqueness ◽  
Normal Extension ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Basic Properties ◽  
Subspace Theorem ◽  
Subnormal Operators ◽  
Minimal Normal Extension

This note provides yet another example of the difficulties that arise when one wants to extend the spectral theory of subnormal operators to subnormal tuples. Several basic properties of a subnormal operator Y remain true for tuples; e.g. the existence and uniqueness of its minimal normal extension N, the spectral inclusion σ(N)⊂ σ(Y)-proved for n-tuples in [4] and generalized to infinite tuples in [5]. However, neither the invariant subspace theorem nor the spectral mapping theorem in the “strong form” as in [3] is known so far for subnormal tuples.

scholarly journals An invariant subspace theorem

1980 ◽  
Vol 38 (3) ◽  
pp. 315-323 ◽  
Author(s):  
Jim Agler
Keyword(s):  
Invariant Subspace ◽  
Subspace Theorem

scholarly journals An invariant-subspace theorem.

1973 ◽  
Vol 20 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Carl Pearcy ◽  
Norberto Salinas
Keyword(s):  
Invariant Subspace ◽  
Subspace Theorem

scholarly journals An invariant subspace theorem

1979 ◽  
Vol 1 (2) ◽  
pp. 425-428 ◽  
Author(s):  
Jim Agler
Keyword(s):  
Invariant Subspace ◽  
Subspace Theorem

scholarly journals Invariant subspace theorems for amenable groups

1989 ◽  
Vol 32 (3) ◽  
pp. 415-430 ◽  
Author(s):  
A. T. Lau ◽  
A. L. T. Paterson ◽  
J. C. S. Wong
Keyword(s):  
Invariant Subspace ◽  
Closed Subspace ◽  
Compact Convex ◽  
Amenable Group ◽  
Dimensional Subspace ◽  
Linear Operators ◽  
Finite Codimension ◽  
Subspace Theorem ◽  
Locally Convex ◽  
Ky Fan

In [5], Ky Fan proved the following remarkable amenability “invariant subspace” theorem:Let G be an amenable group of continuous, invertible linear operators acting on a locally convex space E. Let H be a closed subspace of finite codimension n in E and X⊂E be such that:(i) H and X are G-invariant;(ii) (e + H) ∩X is compact convex for all e ∈ E;(iii) X contains an n-dimensional subspace V of E. Then there exists an n-dimensional subspace of E contained in X and invariant under G.

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