### Impacto

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 |
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Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16420 |

References: | R. M. Aron and J. G. Llavona, Composition of weakly uniformly continuous functions, to appear. R. M. Aron and J. B. Prolla, Polynofnial approxitnation of differentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980), 195-216. W. G. Bade and P. C. Curtis, HOfnofnorphisms of commutative Banach algebras, Amer. J. Math. 82 (1960), 589-608. L. Bers, On rings of analytic functions, Bull. Amer. Math. SOCa 54 (1948), 311-315. D. Clayton, A reduction of the continuous hOlnomorphism problem for F-algebras, Rocky Mountain J. Math. 5 (1975), 337-344. M. M. Day, Norlned linear spaces, 3rd ed., Ergeb. der Math. 21, Springer, Berlín, 1973. J. Dieudonne, Foundations of modern analysis, Academic Press, New York, 1960. G. Glaeser, Fonctions composees differentiables, Ann. of Math. (2) 77 (1963), 193-209. J. Gomez, On local convexity of bounded weak topologies on Banach spaces, Pacific J. Math. 110 (1984),71-75. J. Kelley, General topology, Springer, Berlin, 1975. J. Llavona, Approximation of continuously differentiable functions, Notas de Matematica, 112, North-Holland, Amsterdam, 1986. E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1953). H. H. Schaefer, Topological vector spaces, Springer, Berlin, 1971. R. F. Wheeler, The equicontlnuous weak* topology and semi-reflexivity, Studia Math. 41 (1972), 243-256. S. Yamamuro, Differential calculus in topological linear spaces, Lecture Notes in Math., 374, Springer, Berlin, 1974. |

Deposited On: | 18 Sep 2012 08:31 |

Last Modified: | 07 Feb 2014 09:29 |

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