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Boundaries For Real Banach Algebras

Published online by Cambridge University Press:  20 November 2018

B. V. Limaye
B. V. Limaye*
Affiliation:
Indian Institute of Technology, Bombay, India
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Let A be a commutative real Banach algebra with unit, and MA its maximal ideal space. The existence of the Silov boundary SA for A was established in [5] by resorting to the complexification of A. We give here an intrinsic proof of this result which exhibits the close connection between the absolute values and the real parts of ‘functions’ in A (Theorem 1.3).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 42 - 49
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Ailing, N. L., Real Banach algebras and non-orientable Klein surfaces I, J. Reine Angew. Math. 241 (1970), 200–208.Google Scholar
2. Choquet, G., Lectures on analysis, vol. II (W. A. Benjamin Inc., New York, 1969).Google Scholar
3. Gamelin, T., Uniform algebras (Prentice-Hall, Englew∞d Cliffs, N. J., 1969).Google Scholar
4. Gelfand, I., Raikov, D., and Shilov, G., Commutative normed rings (Chelsea, New York, 1964).Google Scholar
5. Limaye, B. V. and Simha, R. R., Deficiencies of certain real uniform algebras, Can. J. Math. 27 (1975), 121–132.Google Scholar
6. Lund, B., Ideals and subalgebras of a function algebra, Can. J. Math. 26 (1974), 405–411.Google Scholar
7. Rudin, W., Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8 (1957), 39–42.Google Scholar
8. Stout, E. L., The theory of uniform algebras (Bogden-Quigley, Tarrytown-on-Hudson, N. Y., 1971).Google Scholar