Gromov's translation algebras, growth and amenability of operator algebras |
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Authors: | T.G. Ceccherini-Silberstein A.Y. Samet-Vaillant |
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Affiliation: | aDipartimento di Ingegneria, Università del Sannio, C.so Garibaldi 107, 82100 Benevento, Italy;bAvinoam Yellin 16, 95264 Jerusalem, Israel |
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Abstract: | Translation algebras of finitely generated *-algebras of bounded linear operators on a separable Hilbert space are introduced. Two equivalent forms of amenability for finitely generated *-algebras in terms of the existence of Følner sequences are introduced. These are related to the existence of traces on the associated translation algebra and, in the context of C*-algebras, are related to weak-filterability and to the existence of hypertraces. |
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Keywords: | Translation algebras Fø lner sequence Fø lner condition Amenability Finitely generated *-algebras C*-algebras |
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