Spectral invariance of smooth crossed products, and rapid decay locally compact groups |
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Authors: | J I Ronghui and Larry B Schweitzer |
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Institution: | (1) Department of Mathematical Science, IUPUI, 402 N. Blackford Street, 46202-3216 Indianapolis, IN, USA;(2) Department of Mathematics, Arizona State University, 85287-1804 Tempe, AS, USA |
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Abstract: | We show that all rapid-decay locally compact groups are unimodular and that the set of rapid-decay functions on a locally compact rapidly decaying group forms a dense and spectral invariant Fréchet *-subalgebra of the reduced group C
*-algebra. In general, the set of rapid-decay functions on a locally compact strongly rapid-decay group with values in a commutative C
*-algebra forms a dense and spectral invariant Fréchet *-subalgebra of the twisted crossed product C
*-algebra. The spectral invariance property implies that the K-theories of both algebras are naturally isomorphic under inclusion.This project is supported in part by the National Science Foundation Grant #DMS 92-04005. |
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Keywords: | rapid-decay functions locally compact groups C
*-algebras |
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