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Invariant subspace theorems for amenable groups

Published online by Cambridge University Press:  20 January 2009

A. T. Lau ,
A. L. T. Paterson  and
J. C. S. Wong
A. T. Lau
Affiliation:
University of AlbertaAlberta, Canada
A. L. T. Paterson
Affiliation:
University of CalgaryCalgary, Canada
J. C. S. Wong
Affiliation:
University of AberdeenAberdeen, Scotland
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 415 - 430
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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