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Garrido, M. Isabel and Jaramillo Aguado, Jesús Ángel and Prieto Yerro, M. Ángeles
(2000)
*Banach-Stone theorems for Banach manifolds.*
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales., 94
(4).
pp. 525-528.
ISSN 1137-2141

Official URL: http://www.rac.es/4/4_2_2_1.php?id=1

## Abstract

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.

Item Type: | Article |
---|---|

Additional Information: | Monográfico sobre "Perspectivas en Análisis Matemático" |

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

ID Code: | 21627 |

Deposited On: | 31 May 2013 14:49 |

Last Modified: | 12 Dec 2018 15:13 |

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