Biseparating maps between smooth vector-valued functions on Banach manifolds

C J LIAO*, Ya Shu Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

An I-category consists all Banach manifolds as objects and subclasses of continuous functions (with some kind of smoothness) as morphisms. This notion covers, for example, the categories C, Cn, C, and Liploc of all smooth functions, Cn -functions, continuous functions, and local Lipschitz functions. It is shown by Garrido, Jaramillo and Prieto in 2000 that two C -smooth Banach manifolds X and Y are C -diffeomorphic to each other if and only if there is an algebra isomorphism from C(X,R) onto C(Y,R). We extend this result to general abstract I-categories, and from algebra isomorphisms of scalar functions to the maps which are linear, bijective and separating, between vector-valued functions.

Original languageEnglish
Pages (from-to)715-724
Number of pages10
JournalOperators and Matrices
Volume6
Issue number4
DOIs
Publication statusPublished - Dec 2012

Scopus Subject Areas

  • Analysis
  • Algebra and Number Theory

User-Defined Keywords

  • I-category
  • Lipschitz function
  • Separating map
  • Smooth functions

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