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ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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$.


References [Enhancements On Off] (What's this?)

  • [1] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [2] J. Horvath, Topological vector spaces, Addison-Wesley, Reading, Mass., 1966. MR 0205028 (34:4863)
  • [3] T. Husain, Multiplicative functionals on topological algebras, Pitman, Boston, Mass., 1983. MR 704352 (85a:46025)
  • [4] J. A. Jaramillo Algebras de funciones continuas y differenciables. Homomorphismos y interpoblación, Tesis Doctoral, Universidad Complutense de Madrid, 1987.
  • [5] K. Sundaresan and S. Swaminatan, Geometry and nonlinear analysis in Banach spaces, Lecture Notes in Math., vol. 1131, Springer, 1985. MR 793378 (87f:58017)
  • [6] J. C. Wells, Differentiable functions on Banach spaces with Lipschitz derivatives, J. Differential Geometry 8 (1973), 135-152. MR 0370640 (51:6867)

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Additional Information

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

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