{"product_id":"9783540850304","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eMoltó, Aníbal; Orihuela, José; Troyanski, Stanimir; Valdivia, Manuel\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eAbstract topological tools from generalized metric spaces are applied in this volume 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.\u003c\/p\u003e\n\u003cp\u003eMaps from a normed 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. Any one-to-one operator T from a reflexive space X into c\u003csub\u003e0\u003c\/sub\u003e (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.\u003c\/p\u003e\n\u003cp\u003eThis volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2008-10-21\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540850304\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-540-85031-1\u003c\/p\u003e \u003cp\u003eDimensions: cm xcm\u003c\/p\u003e \u003cp\u003ePages: 148\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369798951052,"sku":"9783540850304","price":44.96,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540850304.jpg?v=1775675147","url":"https:\/\/lateknightbooks.com\/products\/9783540850304","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}