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Positive definite functions of Hopf $C^ *$-algebras


Author: Xiu Chi Quan
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
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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.


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Article copyright: © Copyright 1995 American Mathematical Society