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Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions

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Jaramillo Aguado, Jesús Ángel and Jiménez Sevilla, María del Mar and Sánchez González, L. (2014) Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions. Proceedings of the American Mathematical Society, 42 (3). pp. 1075-1087. ISSN 1088-6826

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Official URL: http://www.ams.org/journals/proc/2014-142-03/S0002-9939-2013-11834-4/


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http://www.ams.org/Organisation
http://arxiv.org/pdf/1108.5403v1Organisation


Abstract

In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative defined on M. As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete C-k Finsler manifold M is determined by the algebra C-b(k)(M); (ii) the weak Finsler structure of a separable and complete C-k Finsler manifold M modeled on a Banach space with a Lipschitz and C-k smooth bump function is determined by the algebra C-b(k)(M); (iii) the weak Finsler structure of a C-1 uniformly bumpable and complete C-1 Finsler manifold M modeled on a Weakly Compactly Generated (WCG) Banach space is determined by the algebra C-b(1)(M); and (iv) the isometric structure of a WCG Banach space X with a C-1 smooth bump function is determined by the algebra C-b(1)(X).


Item Type:Article
Uncontrolled Keywords:Differentiable functions; Riemannian-manifolds; Lipschitz functions; approximation; isometries; spaces
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:24700
Deposited On:17 Mar 2014 11:34
Last Modified:17 Mar 2014 11:34

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