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Proceedings of the American Mathematical Society

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A real valued homomorphism on algebras of differentiable functions


Author: Juan Arias-de-Reyna
Journal: Proc. Amer. Math. Soc. 104 (1988), 1054-1058
MSC: Primary 46J15; Secondary 46G20
DOI: https://doi.org/10.1090/S0002-9939-1988-0929406-3
MathSciNet review: 929406
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Abstract: In this paper we prove that, for every homomorphism $ A$ on $ {C^k}\left( E \right)$, there exists $ x \in E$ such that $ A\left( f \right) = f\left( x \right)$ for $ f \in {C^k}\left( E \right)$. Here $ {C^k}\left( E \right)\;\left( {k = 1,2, \ldots, \infty } \right)$ denotes the algebra of all $ k$-times differentiable real functions on a real and separable Banach space $ E$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0929406-3
Article copyright: © Copyright 1988 American Mathematical Society