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020 _a9783540850311
_9978-3-540-85031-1
024 7 _a10.1007/978-3-540-85031-1
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
072 7 _aPBMP
_2thema
082 0 4 _a516.36
_223
100 1 _aMoltó, Aníbal.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 2 _aA Nonlinear Transfer Technique for Renorming
_h[electronic resource] /
_cby Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2009.
300 _aXI, 148 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1951
505 0 _a?-Continuous and Co-?-continuous Maps -- Generalized Metric Spaces and Locally Uniformly Rotund Renormings -- ?-Slicely Continuous Maps -- Some Applications -- Some Open Problems.
520 _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.
650 0 _aGlobal differential geometry.
650 0 _aFunctional analysis.
650 1 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
700 1 _aOrihuela, José.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aTroyanski, Stanimir.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aValdivia, Manuel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540872986
776 0 8 _iPrinted edition:
_z9783540850304
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1951
856 4 0 _uhttps://doi.org/10.1007/978-3-540-85031-1
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11838
_d11838