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ON ITERATED POWERS OF POSITIVE DEFINITE FUNCTIONS

Published online by Cambridge University Press:  16 June 2015

MEHRDAD KALANTAR*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada, K1S 5B6 email mkalanta@math.carleton.ca
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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.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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