LEADER 04739nam 22005415 450 001 9910736984803321 005 20251113182925.0 010 $a3-031-08655-4 024 7 $a10.1007/978-3-031-08655-7 035 $a(MiAaPQ)EBC7077204 035 $a(Au-PeEL)EBL7077204 035 $a(CKB)24739002800041 035 $a(PPN)264191625 035 $a(OCoLC)1342500418 035 $a(DE-He213)978-3-031-08655-7 035 $a(EXLCZ)9924739002800041 100 $a20220823d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRenormings in Banach Spaces $eA Toolbox /$fby Antonio José Guirao, Vicente Montesinos, Václav Zizler 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2022. 215 $a1 online resource (621 pages) 225 1 $aMonografie Matematyczne,$x2297-0274 ;$v75 311 08$aPrint version: Guirao, Antonio José Renormings in Banach Spaces Cham : Springer International Publishing AG,c2022 9783031086540 320 $aIncludes bibliographical references (pages 505-547) and index. 327 $a1 Norms, Normed spaces, Banach spaces -- 2 Some basic definitions and tools -- 3 Equivalent norms -- 4 Basic differentiability in Banach spaces -- 5 Basic convexity -- 6 Some structural properties of Banach spaces -- 7 The use of Smulyan?s tests -- 8 Asplund averaging I -- 9 Tools for renorming -- 10 Renorming of nonseparable Banach spaces -- 11 Examples on C1-smoothness -- 12 Examples on Rotundity -- 13 Nonlinear Transfer Techniques -- 14 Lipschitz functions -- 15 Spaces isomorphic to Hilbert spaces -- 16 Superreflexive spaces -- 17 The Kingdom of Tsirelson?s space -- 18 The L(infinity) spaces -- 19 Higher order smoothness -- 20 James boundaries -- 21 RNP property -- 22 SSD spaces -- 23 Norms with MIP -- 24 Nicely smooth Banach spaces -- 25 Weak Hadamard differentiability -- 26 Fabian?s farm of Lipschitz Asplund spaces -- 27 Fonf?s land of spaces isomorphic to polyhedral spaces -- 28 Hájek?s garden of nice functions on c0(gamma) -- 29 Kottman-type results -- 30 3-space properties -- 31 Polynomials -- 32 Miscellaneous applications -- 33 Miscellaneous topics -- 34 More on WCG spaces and their relatives -- 35 Valdivia compacta -- 36 Renorming classical spaces -- 37 Symmetric norms -- 38 A concise list of coordinates of the relationship -- 39 Some easily formulated open questions on construction of norms in separable spaces -- Index of figures. 330 $aThis monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists anddetailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research. 410 0$aMonografie Matematyczne,$x2297-0274 ;$v75 606 $aFunctional analysis 606 $aFunctional Analysis 615 0$aFunctional analysis. 615 14$aFunctional Analysis. 676 $a515.732 676 $a515.732 700 $aGuirao$b Antonio Jose?$01254628 702 $aMontesinos Julve$b Vicente 702 $aZizler$b Vaclav 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910736984803321 996 $aRenormings in Banach spaces$93363997 997 $aUNINA