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Proceedings of the American Mathematical Society

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Multiplicative linear functionals on convolution algebras


Author: Paul Aizley
Journal: Proc. Amer. Math. Soc. 28 (1971), 65-66
MSC: Primary 20.90
DOI: https://doi.org/10.1090/S0002-9939-1971-0271248-6
MathSciNet review: 0271248
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Abstract: It is shown that semicharacters on the semigroup $ S$ lead in a natural way to multiplicative linear functionals on $ l(S)$, the convolution algebra of all complex valued functions on $ S$. A theorem of D. H. Lehmer and a theorem of M. Tainiter follow as special cases.


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

  • [1] P. Aizley, Structure theory for a class of convolution algebras, University Microfilms, Order #69-16,475, Ann Arbor, Michigan.
  • [2] D. H. Lehmer, On a theorem of von Sterneck, Bull. Amer. Math. Soc. 37 (1931), 723-726. MR 1562243
  • [3] M. Tainiter, Generating functions on idempotent semigroups with application to combinatorial analysis, J. Combinatorial Theory 5 (1968), 273-288. MR 48 #65. MR 0231737 (38:65)
  • [4] E. Hewitt and H. S. Zuckerman, Finite dimensional convolution algebras, Acta. Math. 93 (1955), 67-119. MR 17, 1048. MR 0077522 (17:1048h)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0271248-6
Keywords: Semigroup, semicharacter, idempotents, associates, convolution algebra, multiplicative linear functional
Article copyright: © Copyright 1971 American Mathematical Society

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