Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
MathSciNet review: 1209427
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • Eiichi Abe, Hopf algebras, Cambridge Tracts in Mathematics, vol. 74, Cambridge University Press, Cambridge-New York, 1980. Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka. MR 594432
  • Henri Cartan and Roger Godement, ThĂ©orie de la dualitĂ© et analyse harmonique dans les groupes abĂ©liens localement compacts, Ann. Sci. École Norm. Sup. (3) 64 (1947), 79–99 (French). MR 0023241
  • Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
  • 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.
  • S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613–665. MR 901157
  • ---, Twisted $SU(n)$ group, Tanaka-Krein duality, Invent. Math. 93 (1989), 35-76.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 16W30, 17B37

Retrieve articles in all journals with MSC: 46L05, 16W30, 17B37

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society