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ON ITERATED POWERS OF POSITIVE DEFINITE FUNCTIONS

Part of: Abstract harmonic analysis Locally compact groups and their algebras

Published online by Cambridge University Press:  16 June 2015

MEHRDAD KALANTAR
MEHRDAD KALANTAR*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada, K1S 5B6 email [email protected]
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Abstract

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We prove that if ${\it\rho}$ is an irreducible positive definite function in the Fourier–Stieltjes algebra $B(G)$ of a locally compact group $G$ with $\Vert {\it\rho}\Vert _{B(G)}=1$, then the iterated powers $({\it\rho}^{n})$ as a sequence of unital completely positive maps on the group $C^{\ast }$-algebra converge to zero in the strong operator topology.

Keywords

iterated powerspositive definite functionsunital completely positive maps

MSC classification

Primary: 43A35: Positive definite functions on groups, semigroups, etc.
Secondary: 22D20: Representations of group algebras 22D35: Duality theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 440 - 443
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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