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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Positive definite functions of Hopf $C^ *$-algebras
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by Xiu Chi Quan PDF
Proc. Amer. Math. Soc. 123 (1995), 615-625 Request permission

Abstract:

In this paper we study positive definite functions of Hopf ${C^ \ast }$-algebras. First of all, we introduce Fourier transformation on Hopf ${C^\ast }$-algebras and use Fourier transform to characterize positive definite functions. Then we proceed to study smooth positive definite functions on Hopf ${C^\ast }$-algebras. A complete description of smooth positive definite functions is obtained. Also, a Bochner type result for smooth positive definite functions is proved.
References
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    • X. Quan, Representations of Hopf ${C^\ast }$-algebras. I, II, preprint. —, Krien algebras and structure of Hopf ${C^\ast }$-algebras, preprint. J. Vallin, ${C^\ast }$-Algebre de Hopf et ${C^\ast }$-algebre de Kac, Proc. London Math. Soc. (3) 50 (1985), 131-174.
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    • —, Twisted $SU(n)$ group, Tanaka-Krein duality, Invent. Math. 93 (1989), 35-76.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 615-625
  • MSC: Primary 46L05; Secondary 16W30, 17B37
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1209427-X
  • MathSciNet review: 1209427