A nonlinear transfer technique for renorming

Abstract topological tools from generalized metric spaces are applied in thisvolume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from anormed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Anyone-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. INDICE: 1. Introduction.- 2. Sigma-continuous and Co-sigma continuous maps.- 3. Generalized metric spaces and Locally Uniformly Rotund Renormings.- 4. Sigma-slicely continuous maps.- 5. Some Applications.- 6. Some Open Problems.- References, Index, and List of Symbols.

• ISBN: 978-3-540-85030-4
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 160
• Fecha Publicación: 01/09/2008
• Nº Volúmenes: 1
• Idioma: Inglés