Transition operators on co-compact \(G\)-spaces (Q877795)
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scientific article; zbMATH DE number 5149118
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transition operators on co-compact \(G\)-spaces |
scientific article; zbMATH DE number 5149118 |
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Transition operators on co-compact \(G\)-spaces (English)
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3 May 2007
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The authors prove the following result: Let \(M\) be a complete, co-compact Riemannian manifold. Then \(0\) is in the \(L^2\)-spectrum of the Laplacian of \(M\) if and only if some (equivalently, every) closed quasi-transitive group of isometries of \(M\) is both amenable and unimodular. The same result holds also for Euclidean simplicial complexes.
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\(G\)-space
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proper action
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isometries
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invariant transition operator
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amenability
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