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Positive definite functions of Hopf $ C\sp *$-algebras

Author: Xiu Chi Quan
Journal: Proc. Amer. Math. Soc. 123 (1995), 615-625
MSC: Primary 46L05; Secondary 16W30, 17B37
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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