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Gleason Parts of Real Function Algebras

Published online by Cambridge University Press:  20 November 2018

S. H. Kulkarni  and
B. V. Limaye
S. H. Kulkarni
Affiliation:
Indian Institute of Technology, Bombay, India
B. V. Limaye
Affiliation:
Indian Institute of Technology, Bombay, India
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Although the theory of complex Banach algebras is by now classical, the first systematic exposition of the theory of real Banach algebras was given by Ingelstam [5] as late as 1965. More recently, further attention to real Banach algebras was paid in 1970 [1], where, among other things, the (real) standard algebras on finite open Klein surfaces were introduced. Generalizing these considerations, real uniform algebras were studied in [7] and [6].

In the present paper, an attempt is made to develop the theory of real function algebras (see Section 1 for the definition) along the lines of the complex function algebras. Although the real function algebras are not structurally different from the real uniform algebras introduced in [7], they are easier to deal with since their elements are actually (complex-valued) functions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 1 , 01 February 1981 , pp. 181 - 200
Copyright
Copyright © Canadian Mathematical Society 1981

References

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