Invariant subspace theorems for amenable groups

Author:

Lau A. T.,Paterson A. L. T.,Wong J. C. S.

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference17 articles.

1. Hermitian operators in spaces with indefinite metric;Pontrjagin;Izv. Akad. Nauk SSSR. Ser. Mat.,1963

2. Amenability

3. Moyennes Invariantes et Représentations Unitaires

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