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Jaramillo Aguado, Jesús Ángel and Jiménez Sevilla, María del Mar and Sánchez González, L. (2014) Characterization of a BanachFinsler manifold in terms of the algebras of smooth functions. Proceedings of the American Mathematical Society, 42 (3). pp. 10751087. ISSN 10886826

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Official URL: http://www.ams.org/journals/proc/201414203/S000299392013118344/
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http://www.ams.org/  Organisation 
http://arxiv.org/pdf/1108.5403v1  Organisation 
Abstract
In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete Ck Finsler manifold M is determined by the normed algebra Cb(k)(M) of all realvalued, bounded and Ck smooth functions with bounded derivative defined on M. As a consequence, we obtain: (i) the Finsler structure of a finitedimensional and complete Ck Finsler manifold M is determined by the algebra Cb(k)(M); (ii) the weak Finsler structure of a separable and complete Ck Finsler manifold M modeled on a Banach space with a Lipschitz and Ck smooth bump function is determined by the algebra Cb(k)(M); (iii) the weak Finsler structure of a C1 uniformly bumpable and complete C1 Finsler manifold M modeled on a Weakly Compactly Generated (WCG) Banach space is determined by the algebra Cb(1)(M); and (iv) the isometric structure of a WCG Banach space X with a C1 smooth bump function is determined by the algebra Cb(1)(X).
Item Type:  Article 

Uncontrolled Keywords:  Differentiable functions; Riemannianmanifolds; 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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