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Subordinate and Pseudo-Subordinate Semi-Algebras

Published online by Cambridge University Press:  20 November 2018

Edward J. Barbeau
Edward J. Barbeau*
Affiliation:
The University of Western Ontario, London
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Throughout this paper E denotes a compact Hausdorff space, which, to avoid trivial complications, is assumed to contain at least two points. C(E), with the uniform norm, is the Banach algebra of all continuous real-valued functions defined on E; C+(E) is the set of those functions in C(E) which take only non-negative values. A subset of C(E) is a wedge if and only if it is closed under addition and multiplication by nonnegative scalars; a semi-algebra is a wedge closed under (pointwise) multiplication. The set C+(E) is a semi-algebra, and all semi-algebras considered in this paper are contained in C+(E). For a subset K of C+(E), the closed wedge (semi-algebra) generated by K is the least closed wedge (semi-algebra) containing K.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 212 - 224
Copyright
Copyright © Canadian Mathematical Society 1967

References

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