On the semiring

Author:
Jor-Ting Chan

Journal:
Proc. Amer. Math. Soc. **112** (1991), 171-174

MSC:
Primary 46E25; Secondary 06F25, 46E15

MathSciNet review:
1037205

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Abstract: Let and be locally compact Hausdorff spaces. Let (resp. ) denote the Banach space of all continuous functions on vanishing at infinity on (resp. ) and (resp. ) the semiring of positive operators on (resp. ). We prove that if there exists a semiring isomorphism from onto , then and are homeomorphic. If and are assumed to be compact then the same conclusion holds under the milder condition that is an affine isomorphism and is order bounded.

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1037205-X

Article copyright:
© Copyright 1991
American Mathematical Society