RT Journal Article
T1 Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
A1 Jaramillo Aguado, Jesús Ángel
A1 Jiménez Sevilla, María Del Mar
A1 Sánchez González, L.
AB 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).
PB American Mathematical Society
SN 1088-6826
YR 2014
FD 2014-03
LK https://hdl.handle.net/20.500.14352/33475
UL https://hdl.handle.net/20.500.14352/33475
LA eng
NO DGES (Spain) Project
DS Docta Complutense
RD 7 abr 2025