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Homomorphisms between algebras of differentiable functions in infinite dimensions

Llavona, José G. and Aron, Richard M. and Gómez Gil, Javier (1988) Homomorphisms between algebras of differentiable functions in infinite dimensions. Michigan Mathematical Journal, 35 (2). pp. 163-178. ISSN 0026-2285

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Abstract

Let E and F be two real Banach spaces. For n = 0, 1, ...,1, let Cnw ub(E; F) be the space of n-times continuously differentiable functions f: E ! F such that, for each integer j _ n and each x 2 E, both the jth derivative mapping fj : E ! P(jE; F) and the polynomial fj(x) are weakly uniformly continuous on bounded subsets of E. This paper studies the characterization of the homomorphisms of the type A: Cnw ub(E;R) ! Cm wub(F;R) in terms of mappings g: F00 ! E00 which are differentiable when the biduals E00 and F00 are endowed with their bw_ topologies. The authors prove that every such homomorphism is automatically continuous when the spaces Cnw ub are given their
natural topology.


Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16420
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