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Functionals on Real C(S)

Published online by Cambridge University Press:  20 November 2018

Nicholas Farnum  and
Robert Whitley
Nicholas Farnum
Affiliation:
University of California at Irvine, Irvine, California 92717
Robert Whitley
Affiliation:
University of California at Irvine, Irvine, California 92717
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The maximal ideals in a commutative Banach algebra with identity have been elegantly characterized [5; 6] as those subspaces of codimension one which do not contain invertible elements. Also, see [1]. For a function algebra A, a closed separating subalgebra with constants of the algebra of complex-valued continuous functions on the spectrum of A, a compact Hausdorff space, this characterization can be restated: Let F be a linear functional on A with the property:

(*) For each ƒ in A there is a point s, which may depend on f, for which F(f) = f(s).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 490 - 498
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Browder, A., Introduction to function algebras (Benjamin, 1969).Google Scholar
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4. Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, 1959).Google Scholar
5. Gleason, A., A characterization 0﹜ maximal ideals, J. D'Analyse Math. V.) (1967), 171–172.Google Scholar
6. Kahane, J. P. and Zelazko, W., A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 340–343.Google Scholar
7. Taylor, A., Introduction to Junctional analysis (Wiley, 1958).Google Scholar