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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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Official URL: http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.mmj/1029003744

## 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 |

Deposited On: | 18 Sep 2012 08:31 |

Last Modified: | 27 Jul 2018 10:12 |

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