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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A matrix-valued Choquet-Deny theorem


Authors: Cho-Ho Chu, Titus Hilberdink and John Howroyd
Journal: Proc. Amer. Math. Soc. 129 (2001), 229-235
MSC (1991): Primary 46G10, 45E10, 43A05, 43A25, 31C05
Published electronically: March 29, 2000
MathSciNet review: 1784024
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Abstract:

Let $\sigma$ be a positive matrix-valued measure on a locally compact abelian group $G$ such that $\sigma(G)$ is the identity matrix. We give a necessary and sufficient condition on $\sigma$ for the absence of a bounded non-constant matrix-valued function $f$ on $G$ satisfying the convolution equation $ f *\sigma = f$. This extends Choquet and Deny's theorem for real-valued functions on $G$.


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Additional Information

Cho-Ho Chu
Affiliation: Goldsmiths College, University of London, London SE14 6NW, England
Email: maa01chc@gold.ac.uk

Titus Hilberdink
Affiliation: Goldsmiths College, University of London, London SE14 6NW, England
Email: map01twh@gold.ac.uk

John Howroyd
Affiliation: Goldsmiths College, University of London, London SE14 6NW, England
Email: mas01jdh@gold.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05694-X
PII: S 0002-9939(00)05694-X
Received by editor(s): April 6, 1999
Published electronically: March 29, 2000
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2000 American Mathematical Society