Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-04T18:35:01.813Z Has data issue: false hasContentIssue false

3.—Some Structure Semigroup Results for Arens-Singer Semigroups*

Published online by Cambridge University Press:  14 February 2012

Sheila A. McKilligan
Affiliation:
University of Aberdeen.

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
Copyright
Copyright © Royal Society of Edinburgh 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References to Literature

Arens, R. and Singer, I. M., 1956. Generalized analytic functions. Trans. Am. Math. Soc., 81, 379393.CrossRefGoogle Scholar
Chow, P. S. and White, A. J., 1971. The structure semigroup of some convolution measure algebras. Q. Jl Math., 11, 221229.CrossRefGoogle Scholar
De Leeuw, K. and Glicksberg, I., 1961a. Applications of almost periodic compactifications. Acta Math., 105, 6397.CrossRefGoogle Scholar
De Leeuw, K. 1961 b. Almost periodic functions on semigroups. Acta Math., 105, 99140.CrossRefGoogle Scholar
Hewitt, E. and Ross, K. A., 1963. Abstract Harmonic Analysis, I. Heidelberg: Springer.Google Scholar
Hewitt, E., 1970. Abstract Harmonic Analysis, II. 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, 265274.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, 679683.CrossRefGoogle Scholar
Ramirez, D. E., 1968. The measure algebra as an operator algebra. Can. J. Math., 20, 13911396.CrossRefGoogle Scholar
Rennison, J. F., 1969. Arens products and measure algebras. J. Lond. Math. Soc., 44, 369377.CrossRefGoogle Scholar
Rickart, C. E., 1960. General Theory of Banach Algebras. New York: Van Nostrand.Google Scholar
Rieffel, M. A., 1965. A characterisation of commutative group algebras and measure algebras. Trans. Am. Math. Soc., 116, 3265.CrossRefGoogle Scholar
Rudin, W., 1967. Fourier Analysis on Groups. New York: Interscience.Google Scholar
Stromberg, K., 1959. A note on the convolution of regular measures. Math. Scand., 7, 347352.CrossRefGoogle Scholar
Taylor, J. L., 1965. The structure of convolution measure algebras. Trans. Am. Math. Soc., 119, 150166.CrossRefGoogle Scholar