Uniform equicontinuity, multiplier topology and continuity of convolution

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• 作者：Matthias Neufang (1) (2)
  Jan Pachl (3)
  Pekka Salmi (4)
  
  1. School of Mathematics and Statistics ; Carleton University ; Ottawa ; ON ; K1S 5B6 ; Canada
  2. Laboratoire de Math茅matiques Paul Painlev茅 (UMR CNRS 8524) ; Universit茅 Lille 1-Sciences et Technologies ; UFR de Math茅matiques ; 59655 ; Villeneuve d鈥橝scq Cedex ; France
  3. Fields Institute ; 222 College Street ; Toronto ; ON ; M5T 3J1 ; Canada
  4. Department of Mathematical Sciences ; University of Oulu ; PL 3000 ; 90014 ; Oulu ; Finland
  
• 关键词：22D15 ; 43A10 ; 43A15 ; 43A20 ; Topological and locally compact groups ; Left uniformly continuous functions ; Uniform equicontinuity ; Measure algebra ; Continuity of convolution
• 刊名：Archiv der Mathematik
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：104
• 期：4
• 页码：367-376
• 全文大小：201 KB
• 参考文献：1. Caby, E. (1987) A note on the convolution of probability measures. Proc. Amer. Math. Soc. 99: pp. 549-554 CrossRef
  2. Csisz谩r, I. (1971) On the weak* continuity of convolution in a convolution algebra over an arbitrary topological group. Studia Sci. Math. Hungar. 6: pp. 27-40
  3. H.G. Dales, Banach algebras and automatic continuity, Clarendon Press, Oxford University Press, 2000.
  4. Gromov, M., Milman, V.D. (1983) A topological application of the isoperimetric inequality. Amer. J. Math. 105: pp. 843-854 CrossRef
  5. E. Hewitt and K.A. Ross, Abstract harmonic analysis, Vol. 1. 2nd edition, Springer, 1979.
  6. Lau, A.T.-M. (1986) Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups. Math. Proc. Cambridge Philos. Soc. 99: pp. 273-283 CrossRef
  7. Neufang, M. (2004) A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis. Arch. Math. (Basel) 82: pp. 164-171 CrossRef
  8. J. Pachl, Uniform spaces and measures. Fields Institute Monographs, Springer, 2013.
  9. V. Pestov, Dynamics of infinite-dimensional groups. The Ramsey鈥揇voretzky鈥揗ilman phenomenon. American Mathematical Society, 2006.
  10. J.S. Pym, The convolution of linear functionals. Proc. London Math. Soc. (3) 14 (1964), 431鈥?44.
  11. Pym, J.S. (1965) The convolution of linear functionals in spaces of bounded functions. Proc. London Math. Soc. 15: pp. 84-104
  12. Salmi, P. (2010) Joint continuity of multiplication on the dual of the left uniformly continuous functions. Semigroup Forum 80: pp. 155-163 CrossRef
  13. Sentilles, F.D., Taylor, D.C. (1969) Factorization on Banach algebras and the general strict topology. Trans. Amer. Math. Soc. 142: pp. 141-152 CrossRef
  14. Wendel, J.G. (1952) Left centralizers and isomorphisms of group algebras. Pacific J. Math 2: pp. 251-261 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

We characterise bounded uniformly equicontinuous sets of functions on locally compact groups in terms of uniform factorisation. We apply this result to study the continuity of the convolution product on the dual LUC(G)* of the space of bounded left uniformly continuous functions with the topology of uniform convergence on bounded uniformly equicontinuous sets. When restricted to the space of finite Radon measures on a locally compact group, this is the right multiplier topology. For any topological group, the convolution is jointly continuous on bounded sets in the measure algebra. It is jointly continuous on all of LUC(G)* when G is a locally compact SIN group.