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AN EXTENSION OF THE BANACH–STONE THEOREM

Part of: Linear function spaces and their duals Special classes of linear operators Calculus on manifolds; nonlinear operators

Published online by Cambridge University Press:  08 November 2017

MOHAMMED BACHIR
MOHAMMED BACHIR*
Affiliation:
Laboratoire SAMM 4543, Université Paris 1, Panthéon-Sorbonne, Centre P.M.F., 90 rue Tolbiac, 75634 Paris cedex 13, France email Mohammed.Bachir@univ-paris1.fr
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Abstract

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We establish an extension of the Banach–Stone theorem to a class of isomorphisms more general than isometries in a noncompact framework. Some applications are given. In particular, we give a canonical representation of some (not necessarily linear) operators between products of function spaces. Our results are established for an abstract class of function spaces included in the space of all continuous and bounded functions defined on a complete metric space.

Keywords

Banach–Stone theoremfunction spacescomposition operatorisometries and isomorphismsFréchet and Gâteaux differentiability on Banach spacesduality

MSC classification

Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Secondary: 47B33: Composition operators 58C20: Differentiation theory (Gateaux, Fréchet, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 1 , August 2018 , pp. 1 - 23
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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