Banach spaces and their applications in analysis. Nigel Kalton's 60th birthday PDF
Preview Banach spaces and their applications in analysis. Nigel Kalton's 60th birthday
Banach Spaces and their Applications in Analysis Nigel J. Kalton Banach Spaces and their Applications in Analysis Proceedings of the International Conference at Miami University (cid:2) May 22 27, 2006 In Honor of Nigel Kalton’s 60th Birthday Editors Beata Randrianantoanina Narcisse Randrianantoanina ≥ Walter de Gruyter · Berlin · New York Editors BeataRandrianantoanina NarcisseRandrianantoanina DepartmentofMathematicsandStatistics DepartmentofMathematicsandStatistics MiamiUniversity MiamiUniversity Oxford,OH45056,USA Oxford,OH45056,USA E-mail:[email protected] E-mail:[email protected] Keywords:applicationsofBanachspacetheory,approximationtheory,functionalcalculus,algebraicmethods inBanachspaces,homologicalmethodsinBanachspaces,isomorphictheory,nonlineartheory Mathematics Subject Classification 2000: primary 46-06, 46N10, 46N20, 46N30, 46N40; secondary 46A22, 46B10,46B20,46E39,47H09 (cid:2)(cid:2)Printedonacid-freepaperwhichfallswithintheguidelinesofthe ANSItoensurepermanenceanddurability. LibraryofCongressCataloging-in-PublicationData A CIP catalogue record for this book is available from the LibraryofCongress. ISBN 978-3-11-019449-4 BibliographicinformationpublishedbytheDeutscheNationalbibliothek TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie; detailedbibliographicdataareavailableintheInternetathttp://dnb.d-nb.de. ”Copyright2007byWalterdeGruyterGmbH&Co.KG,10785Berlin,Germany. Allrightsreserved,includingthoseoftranslationintoforeignlanguages.Nopartofthisbookmayberepro- ducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher. PrintedinGermany. Coverdesign:ThomasBonnie,Hamburg. Printingandbinding:Hubert&Co.GmbH&Co.KG,Göttingen. Preface StefanBanachoncesaid: “Amathematicianisapersonwhocanfindanalogiesbetweentheorems;a bettermathematicianisonewhocanseeanalogiesbetweenproofs;andthe bestmathematiciancannoticeanalogiesbetweentheories. Onecanimag- inethattheultimatemathematicianisonewhocanseeanalogiesbetween analogies.” Accordingtothisdefinition,NigelKaltonisoneoftheultimatemathematicians. In his work, Kalton finds underlying connections between seemingly unrelated areas of mathematics. He has been immensely successful in applying Banach space methods to numerous problems in analysis. Thus, we honor him on the occasion of his 60th birthdayin2007. As evidenced by the participation of over 160 mathematicians from around the world, it is clear that our community sees the power and potential of Banach space methods in solving a broad array of analysis problems. Indeed, in recent years there has been a surge of profound new developments in analysis – developments whose connecting thread is the use of Banach space methods. Many problems seemingly far from classical geometry of Banach spaces have been solved using Banach space techniques. In this conference, specialists who have been instrumental in these new develop- ments were brought together. The emphasis of the conference was on applications of Banachspacemethodsinthefollowingareas: 1. Nonlinear theory (Lipschitz classifications of Banach/metric spaces, linear pro- grammingmethodsandrelatedtopics); 2. IsomorphictheoryofBanachspacesincludingconnectionswithcombinatoricsand settheory; 3. AlgebraicandhomologicalmethodsinBanachspaces; 4. ApproximationtheoryandalgorithmsinBanachspaces(greedyalgorithms,inter- polationetc.); 5. Functionalcalculusandapplicationstopartialdifferentialequations. At the conference there were 15 plenary talks giving a broad overview of various areas where Banach space methods found applications. In addition, 105 talks were delivered in specialized sessions. These Proceedings reflect the conference. They include 11 papers by plenary speakers and 16 specialized papers by participants of the conference. We especially thank Gilles Godefroy for writing an excellent article surveying the vast work of Nigel Kalton. Godefroy describes many of the important breakthroughs in different areas of analysis and presents open problems for further research. vi Preface We thank Miami University for hosting the conference and providing substantial support for a successful meeting. We especially thank Mark A. Smith, chair of the Department of Mathematics and Statistics at Miami University for both financial and logistical support. We thank the following units of Miami University for financial grants in support of the conference: the Office of the Dean of Arts and Science, the OfficeoftheDeanofEngineeringandAppliedScience,theOfficeoftheProvostand theInternationalVisitingScholarExchangeFund. WethankMarkAshbaugh,chairoftheDepartmentofMathematicsattheUniver- sityofMissouri-Columbia,andCurator’sProfessorFundfromUniversityofMissouri- Columbiafortheirfinancialsupport. WethanktheAmericanMathematicalSocietyandaprivatedonorfortheirfinancial contributions. We thank the following publishers who generously provided books for display at theconference: CambridgeUniversityPress,PrincetonUniversityPressandSpringer- Verlag. WealsothankBrillScienceLibraryofMiamiUniversityforlendingadditional booksfordisplay. WethanktheNationalScienceFoundation,whosegrantprovidedtravelsupportfor manyconferenceparticipants. Wethankthesupportstaff,especiallyLindaFerriell,forhelpingtoruntheconfer- encesmoothly. Last, but most important of all, we thank all the speakers and participants of the conferencewhomadeitasuccess. Oxford,Ohio,June2007 BeataRandrianantoanina NarcisseRandrianantoanina Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v GILLES GODEFROY AglimpseatNigelKalton’swork . . . . . . . . . . . . . . . . . . . . . . . . . . 1 YURI BRUDNYI Multivariatefunctionsofbounded(k,p)-variation . . . . . . . . . . . . . . . . . 37 JESU´S M. F. CASTILLO, YOLANDA MORENO TwisteddualitiesinBanachspacetheory . . . . . . . . . . . . . . . . . . . . . . 59 STEPHEN J. DILWORTH, BU¨NYAMIN SARI Orliczsequencespaceswithdenumerablesetsofsymmetricsequences . . . . . . 77 VALENTIN FERENCZI, CHRISTIAN ROSENDAL ComplexityandhomogeneityinBanachspaces . . . . . . . . . . . . . . . . . . 83 JORAM LINDENSTRAUSS, DAVID PREISS, JAROSLAV TISˇER Fre´chetdifferentiabilityofLipschitzmapsandporoussetsinBanachspaces . . . 111 JAN VAN NEERVEN, MARK VERAAR, LUTZ WEIS ConditionsforstochasticintegrabilityinUMDBanachspaces . . . . . . . . . . 125 EDWARD ODELL, THOMAS SCHLUMPRECHT, ANDRA´S ZSA´K AnewinfinitegameinBanachspaceswithapplications . . . . . . . . . . . . . 147 GIDEON SCHECHTMAN Extremalconfigurationsformomentsofsumsofindependentpositiverandom variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 VLADIMIR TEMLYAKOV GreedyapproximationinBanachspaces . . . . . . . . . . . . . . . . . . . . . 193 ROMAN VERSHYNIN Someproblemsinasymptoticconvexgeometryandrandommatricesmotivated bynumericalalgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 LIPI R. ACHARYA, MANJUL GUPTA OnKolmogorovnumbersofmatrixtransformations . . . . . . . . . . . . . . . 219 MAR´IA D. ACOSTA, LUIZA A. MORAES OnboundariesforspacesofholomorphicfunctionsontheunitballofaBanach space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 viii TableofContents GEORGE ANDROULAKIS, FRANK SANACORY SomeequivalentnormsontheHilbertspace . . . . . . . . . . . . . . . . . . . 241 PRADIPTA BANDYOPADHYAY, BOR-LUH LIN, T. S. S. R. K. RAO BallproximinalityinBanachspaces. . . . . . . . . . . . . . . . . . . . . . . .251 EARL BERKSON, OSCAR BLASCO, MAR´IA J. CARRO, THOMAS A. GILLESPIE Discretizationversustransferenceforbilinearoperators . . . . . . . . . . . . . 265 OLGA A. BREZHNEVA, ALEXEY A. TRET’YAKOV ImplicitfunctiontheoremsfornonregularmappingsinBanachspaces. Exitfromsingularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 STEFAN CZERWIK, MACIEJ PRZYBYŁA AgeneralBakersuperstabilitycriteriumfortheD’Alembertfunctionalequation . 303 JAKUB DUDA, OLGA MALEVA Metricderivednumbersandcontinuousmetricdifferentiabilityvia homeomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 RICHARD J. FLEMING Bohnenblust’stheoremandnorm-equivalentcoordinates . . . . . . . . . . . . . 331 MARCOS GONZA´LEZ, MAREK WO´JTOWICZ AnisometricformofatheoremofLindenstraussandRosenthalonquotients of(cid:2) (Γ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 1 TUOMAS P. HYTO¨NEN AspectsofprobabilisticLittlewood–PaleytheoryinBanachspaces . . . . . . . . 343 ANNA KAMIN´SKA, ANCA M. PARRISH Theq-concavityandq-convexityconstantsinLorentzspaces . . . . . . . . . . . 357 GRZEGORZ LEWICKI, LESŁAW SKRZYPEK OnpropertiesofChalmers–Metcalfoperators . . . . . . . . . . . . . . . . . . . 375 RENXING NI ApproximatingfixedpointsofasymptoticallyΦ-hemicontractivetypemappings . 391 TIMUR OIKHBERG SomepropertiesrelatedtotheDaugavetproperty . . . . . . . . . . . . . . . . . 399 HE´CTOR N. SALAS PathologicalhypercyclicoperatorsII . . . . . . . . . . . . . . . . . . . . . . . 403 BORIS SHEKHTMAN Onperturbationsofidealcomplements . . . . . . . . . . . . . . . . . . . . . . 413 JARNO TALPONEN AsymptoticallytransitiveBanachspaces . . . . . . . . . . . . . . . . . . . . . 423 TableofContents ix Photooftheparticipants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .440 Participantsoftheconference . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Plenarytalks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .446 Talksinspecialsessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
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