LEADER 03553nam 22006015 450 001 996466523203316 005 20200701024508.0 010 $a3-540-85031-7 024 7 $a10.1007/978-3-540-85031-1 035 $a(CKB)1000000000546308 035 $a(SSID)ssj0000447003 035 $a(PQKBManifestationID)11268015 035 $a(PQKBTitleCode)TC0000447003 035 $a(PQKBWorkID)10504819 035 $a(PQKB)11568267 035 $a(DE-He213)978-3-540-85031-1 035 $a(MiAaPQ)EBC3063555 035 $a(PPN)131119095 035 $a(EXLCZ)991000000000546308 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 12$aA Nonlinear Transfer Technique for Renorming$b[electronic resource] /$fby Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia 205 $a1st ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (XI, 148 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1951 300 $aISSN 0075-8434 for print edition. 311 $a3-540-85030-9 320 $aIncludes bibliographical references and index. 327 $a?-Continuous and Co-?-continuous Maps -- Generalized Metric Spaces and Locally Uniformly Rotund Renormings -- ?-Slicely Continuous Maps -- Some Applications -- Some Open Problems. 330 $aAbstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1951 606 $aDifferential geometry 606 $aFunctional analysis 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aDifferential geometry. 615 0$aFunctional analysis. 615 14$aDifferential Geometry. 615 24$aFunctional Analysis. 676 $a516.36 700 $aMoltó$b Aníbal$4aut$4http://id.loc.gov/vocabulary/relators/aut$0602761 702 $aOrihuela$b José$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTroyanski$b Stanimir$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aValdivia$b Manuel$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466523203316 996 $aNonlinear transfer technique for renorming$91014875 997 $aUNISA