RT Journal Article
T1 Banach-Stone theorems for Banach manifolds
A1 Garrido Carballo, María Isabel
A1 Jaramillo Aguado, Jesús Ángel
A1 Prieto Yerro, M. Ángeles
AB 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.
PB Real Academia de Ciencias Exactas, Físicas y Naturales
SN 1137-2141
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/58531
UL https://hdl.handle.net/20.500.14352/58531
NO Monográfico sobre "Perspectivas en Análisis Matemático"Research partially supported by DGES grants PB96/1262 and PB96/0607
DS Docta Complutense
RD 10 dic 2025