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Compactly bounded convolutions of measures

Author: Adam W. Parr
Journal: Proc. Amer. Math. Soc. 130 (2002), 2661-2667
MSC (2000): Primary 43A99
Published electronically: March 13, 2002
MathSciNet review: 1900874
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Abstract: In this paper we extend classical results concerning generalized convolution structures on measure spaces. Given a locally compact Hausdorff space $X$, we show that a compactly bounded convolution of point masses that is continuous in the topology of weak convergence with respect to $C_{c}(X)$ can be extended to a general convolution of measures which is separately continuous in the topology of weak convergence with respect to $C_{b}(X)$.

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  • [1] R.C Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. (5) (1958), 95-104. MR 21:4350
  • [2] E. Hewitt, K.A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer-Verlag, New York, 1979. MR 81k:43001
  • [3] R.I. Jewett, Spaces with an abstract convolution of measures, Advances in Math. (18) (1975), 1-101. MR 52:14840
  • [4] E.A. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. (71) (1955), 151-182. MR 13:54f
  • [5] W. Rudin, Functional Analysis, Second edition, McGraw-Hill, New York, 1991. MR 92k:46001
  • [6] A. Parr, Signed Hypergroups, Ph.D. Thesis, University of Oregon (1997).
  • [7] J.S. Pym, Weakly separately continuous measure algebras, Math. Ann. (175) (1968), 207-219. MR 36:5715
  • [8] M. Rösler, Convolution algebras which are not necessarily positivity preserving, Contemp. Math. (183) (1995), 299-318. MR 96c:43006
  • [9] M. Rösler, Bessel-type signed hypergroups on $\Re $, Probability measures on groups and related structures, XI (Oberwolfach 1994) (1995), 292-304. MR 97j:43004
  • [10] M. Rösler, M. Voit, Partial Characters and Signed Quotient Hypergroups, Canadian J. Math. (51(1)) (1999), 96-116. MR 2000g:43008
  • [11] K.A. Ross, Signed hypergroups--a survey, Contemp. Math. (183) (1995), 319-329. MR 96c:43007

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Additional Information

Adam W. Parr
Affiliation: Department of Mathematics, University of the Virgin Islands, St. Thomas, United States Virgin Islands

Keywords: Signed hypergroup, convolution, strict topology
Received by editor(s): April 6, 2001
Published electronically: March 13, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society

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