No CrossRef data available.
Article contents
3.—Some Structure Semigroup Results for Arens-Singer Semigroups*
Published online by Cambridge University Press: 14 February 2012
Synopsis
In this paper we discuss the structure semigroup of the L1-algebra of an Arens-Singer semigroup. Arising from this study we provide a complete and rather unexpected description of a nontrivial structure semigroup. We then link the above ideas with that of the almost periodic compactification of the semigroup.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 71 , Issue 1 , 1972 , pp. 31 - 42
- Copyright
- Copyright © Royal Society of Edinburgh 1972
References
References to Literature
Arens, R. and Singer, I. M., 1956. Generalized analytic functions. Trans. Am. Math. Soc., 81, 379–393.CrossRefGoogle Scholar
Chow, P. S. and White, A. J., 1971. The structure semigroup of some convolution measure algebras. Q. Jl Math., 11, 221–229.CrossRefGoogle Scholar
De Leeuw, K. and Glicksberg, I., 1961a. Applications of almost periodic compactifications. Acta Math., 105, 63–97.CrossRefGoogle Scholar
De Leeuw, K. 1961 b. Almost periodic functions on semigroups. Acta Math., 105, 99–140.CrossRefGoogle Scholar
Hewitt, E. and Ross, K. A., 1963. Abstract Harmonic Analysis, I. Heidelberg: Springer.Google Scholar
Hofmann, K. H. and Mostert, P. S., 1966. Elements of Compact Semigroups. Columbus, Ohio: Merrill.Google Scholar
Kaashoek, M. A. and West, T. T., 1969. Compact semigroups in commutative Banach algebras. Proc. Camb. Phil. Soc., 66, 265–274.CrossRefGoogle Scholar
Loomis, L. H., 1953. An Introduction to Abstract Harmonic Analysis. New York: Van Nostrand.Google Scholar
Petrich, M., 1962. Semicharacters of the cartesian product of two semigroups. Pacific J. Math., 12, 679–683.CrossRefGoogle Scholar
Ramirez, D. E., 1968. The measure algebra as an operator algebra. Can. J. Math., 20, 1391–1396.CrossRefGoogle Scholar
Rennison, J. F., 1969. Arens products and measure algebras. J. Lond. Math. Soc., 44, 369–377.CrossRefGoogle Scholar
Rieffel, M. A., 1965. A characterisation of commutative group algebras and measure algebras. Trans. Am. Math. Soc., 116, 32–65.CrossRefGoogle Scholar
Stromberg, K., 1959. A note on the convolution of regular measures. Math. Scand., 7, 347–352.CrossRefGoogle Scholar
Taylor, J. L., 1965. The structure of convolution measure algebras. Trans. Am. Math. Soc., 119, 150–166.CrossRefGoogle Scholar