LEADER 05021nam 2200601 a 450 001 9910967710203321 005 20251117091016.0 010 $a1-61470-561-5 035 $a(CKB)2550000000047596 035 $a(EBL)3020235 035 $a(SSID)ssj0000569647 035 $a(PQKBManifestationID)12252049 035 $a(PQKBTitleCode)TC0000569647 035 $a(PQKBWorkID)10541838 035 $a(PQKB)11423068 035 $a(MiAaPQ)EBC3020235 035 $a(Au-PeEL)EBL3020235 035 $a(CaPaEBR)ebr10676371 035 $a(OCoLC)751977960 035 $a(BIP)43288775 035 $a(BIP)18717651 035 $a(EXLCZ)992550000000047596 100 $a20090708d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNon-Archimedean linear operators and applications /$fToka Diagana 205 $a1st ed. 210 $aHauppauge, N.Y. $cNova Science ;$aLancaster $cGazelle [distributor]$d2009 215 $a1 online resource (108 p.) 300 $aDescription based upon print version of record. 311 08$a1-60456-494-6 320 $aIncludes bibliographical references and index. 327 $aIntro -- NON-ARCHIMEDEANLINEAROPERATORSANDAPPLICATIONS -- NON-ARCHIMEDEANLINEAROPERATORSANDAPPLICATIONS -- Contents -- Preface -- Chapter1Non-ArchimedeanValuedFields -- 1.1Introduction -- 1.2Non-ArchimedeanValuedFields -- 1.2.1BasicDefinitions -- 1.2.2Thet-VectorSpaceKt -- 1.3ConstructionofQp -- 1.3.1Introduction -- 1.3.2TheFieldQp -- 1.3.3ConvergenceofPowerSeriesoverQp -- 1.4ConstructionofK((x)) -- 1.5BibliographicalNotes -- Chapter2Non-ArchimedeanBanachandHilbertSpaces -- 2.1Non-ArchimedeanBanachSpaces -- 2.1.1BasicDefinitions -- 2.1.2ExamplesofNon-ArchimedeanBanachSpaces -- 2.2FreeBanachSpaces -- 2.2.1Definitions -- 2.2.2Examples -- 2.3Non-ArchimedeanHilbertSpaces -- 2.3.1Introduction -- 2.3.2Non-ArchimedeanHilbertSpaces -- 2.3.3TheHilbertSpaceEw1×Ew2×...×Ewt -- 2.4BibliographicalNotes -- Chapter3Non-ArchimedeanBoundedLinearOperators -- 3.1Introduction -- 3.2BoundedLinearOperatorsonNon-ArchimedeanBanachSpaces -- 3.2.1BasicDefinitions -- 3.2.2Examples -- 3.2.3TheBanachAlgebraB(X) -- 3.2.4FurtherPropertiesofBoundedLinearOperators -- 3.3BoundedLinearOperatorsonHilbertSpacesEw -- 3.3.1Introduction -- 3.3.2RepresentationofBoundedOperatorsByInfiniteMatrices -- 3.3.3ExistenceoftheAdjoint -- 3.3.4ExamplesofBoundedOperatorswithnoAdjoint -- 3.4PerturbationofBases -- 3.4.1Example -- 3.5Hilbert-SchmidtOperators -- 3.5.1BasicDefinitions -- 3.5.2FurtherPropertiesofHilbert-SchmidtOperators -- 3.5.3CompletelyContinuousOperators -- 3.5.4Trace -- 3.5.5Examples -- 3.6OpenProblems -- 3.7BibliographicalNotes -- Chapter4Non-ArchimedeanUnboundedLinearOperators -- 4.1Introduction -- 4.2BasicDefinitions -- 4.2.1Example -- 4.2.2ExistenceoftheAdjoint -- 4.2.3ExamplesofUnboundedOperatorsWithnoAdjoint -- 4.3ClosedLinearOperatorsonEw -- 4.4DiagonalOperatorsonEw -- 4.5OpenProblems -- 4.6BibliographicalNotes -- Chapter5Non-ArchimedeanBilinearForms -- 5.1Introduction. 327 $a5.2BasicDefinitions -- 5.2.1ContinuousLinearFunctionalsonEw -- 5.2.2BoundedBilinearFormsonEw×Ew -- 5.2.3UnboundedBilinearFormsonEw×Ew -- 5.3ClosedandClosablenon-ArchimedeanBilinearForms -- 5.3.1ClosednessoftheFormSum -- 5.3.2Constructionofanon-ArchimedeanHilbertSpaceUsingQuadraticForms -- 5.3.3FurtherPropertiesoftheClosure -- 5.4RepresentationofBilinearFormsonEw×EwbyLinearOperators -- 5.5BibliographicalNotes -- Chapter6FunctionsofSomeSelf-adjointLinearOperatorsonEw -- 6.1Introduction -- 6.2ProductsandSumsofDiagonalOperators -- 6.3IntegerPowersofDiagonalOperators -- 6.4FunctionsofSelf-AdjointOperators -- 6.5FunctionsofSomeSymmetricSquareMatricesOverQp×Qp -- 6.5.1ThePowersoftheMatrixT -- 6.5.2ExponentialoftheMatrixT -- 6.6OpenProblems -- 6.7BibliographicalNotes -- Chapter7One-ParameterFamilyofBoundedLinearOperatorsonFreeBanachSpaces -- 7.1Introduction -- 7.2BasicDefinitions -- 7.3Propertiesofnon-ArchimedeanC0-Groups -- 7.4ExistenceofSolutionstoSomep-adicDifferentialEquations -- 7.5OpenProblems -- 7.6BibliographicalNotes -- References -- Index -- Blank Page. 330 $aThis self-contained book provides the reader with a comprehensive presentation of recent investigations on operator theory over non-Archimedean Banach and Hilbert spaces. This includes, non-archimedean valued fields, bounded and unbounded linear operators, bilinear forms, functions of linear operators and one-paramter families of bounded linear operators on free branch spaces. 606 $aLinear operators 606 $aBanach spaces 606 $aHilbert space 615 0$aLinear operators. 615 0$aBanach spaces. 615 0$aHilbert space. 676 $a515.7246 700 $aDiagana$b Toka$0756010 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910967710203321 996 $aNon-Archimedean linear operators and applications$94475991 997 $aUNINA