%0 Journal Article
%A Garrido, M. Isabel
%A Jaramillo Aguado, Jesús Ángel
%A Prieto Yerro, M. Ángeles
%T Banach-Stone theorems for Banach manifolds
%D 2000
%@ 1137-2141
%U https://hdl.handle.net/20.500.14352/58531
%X This short article addresses natural problems such as this one: Let M  and N  be two Banach manifolds such that the algebras of real-analytic functions on M  and N  are isomorphic as algebras. Does it follow that M  and N  are real-analytic isomorphic? The obvious way to attack the question is to identify, if possible, the sets M  and N  with the spectra of the relevant algebras, and then to transpose the algebra isomorphism. This often works, as shown in this article, but not always: an interesting example (Proposition 6) is given by M=c 0 (Γ) , where Γ  is an uncountable set, and N=M∖{0} . This should be compared with P. Hajek's theorem [Israel J. Math. 104 (1998), 17–27; which asserts that there is no C 2   smooth function on the space c 0 (Γ)  which vanishes in exactly one point.
%~