Homomorphisms between algebras of differentiable functions in infinite dimensions



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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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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
Deposited On:18 Sep 2012 08:31
Last Modified:27 Jul 2018 10:12

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