RT Journal Article
T1 Homomorphisms between algebras of differentiable functions in infinite dimensions
A1 Llavona, José G.
A1 Aron, Richard M.
A1 Gómez Gil, Javier
AB 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 theirnatural topology.
PB Michigan Mathematical Journal
SN 0026-2285
YR 1988
FD 1988
LK https://hdl.handle.net/20.500.14352/57534
UL https://hdl.handle.net/20.500.14352/57534
LA eng
NO C.A.I.C.Y.T (Spain)
DS Docta Complutense
RD 17 abr 2025