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A Class of Translation Lattices

Published online by Cambridge University Press:  20 November 2018

John C. Taylor
John C. Taylor*
Affiliation:
McGill University
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Let E be a completely regular space, let C* denote the Banach algebra of continuous bounded real-valued functions on E, and let A* denote a Banach subalgebra which contains the constant function 1. Let

The purpose of this note is to discuss some properties of the subsets L(A*) of the ring C of continuous real-valued functions on E. They arose out of an unsuccessful attempt to distinguish C* from its Banach subalgebras.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 31 - 39
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Henriksen, M. and Johnson, D. G., On the structure of a class of archimedean lattice ordered algebras, Fund. Math., 50 (1961), 73–94.Google Scholar
2. Isbell, J. R., Algebras of uniformly continuous functions, Ann. Math., 68 (1958), 96–125.Google Scholar
3. Shirota, T., A class of topological spaces, Osaka Math. J., 4 (1952), 23–40.Google Scholar