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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Functional calculus and $*$-regularity of a class of Banach algebras
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by Chi-Wai Leung and Chi-Keung Ng PDF
Proc. Amer. Math. Soc. 134 (2006), 755-763 Request permission

Abstract:

Suppose that $(A,G,\alpha )$ is a $C^*$-dynamical system such that $G$ is of polynomial growth. If $A$ is finite dimensional, we show that any element in $K(G;A)$ has slow growth and that $L^1(G, A)$ is $*$-regular. Furthermore, if $G$ is discrete and $\pi$ is a “nice representation” of $A$, we define a new Banach $*$-algebra $l^1_{\pi }(G, A)$ which coincides with $l^1(G;A)$ when $A$ is finite dimensional. We also show that any element in $K(G;A)$ has slow growth and $l^1_{\pi }(G, A)$ is $*$-regular.
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Additional Information
  • Chi-Wai Leung
  • Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Hong Kong
  • Email: cwleung@math.cuhk.edu.hk
  • Chi-Keung Ng
  • Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
  • Email: ckng@nankai.edu.cn
  • Received by editor(s): June 23, 2004
  • Received by editor(s) in revised form: August 19, 2004, and October 13, 2004
  • Published electronically: July 19, 2005
  • Additional Notes: This work was jointly supported by Hong Kong RGC Direct Grant and the National Natural Science Foundation of China (10371058)
  • Communicated by: David R. Larson
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 755-763
  • MSC (2000): Primary 47A60, 32A65
  • DOI: https://doi.org/10.1090/S0002-9939-05-08025-1
  • MathSciNet review: 2180894