c space

In the mathematical field of functional analysis, the space denoted by c is the vector space of all convergent sequencesof real numbers or complex numbers.When equipped with the uniform norm:the spacebecomes a Banach space.It is a closed linear subspace of the space of bounded sequences,ℓ, and contains as a closed subspace the Banach spaceof sequences converging to zero.The dual ofis isometrically isomorphic toℓis reflexive.In the first case, the isomorphism ofℓℓthen the pairing with an elementThis is the Riesz representation theorem on the ordinalωThis mathematical analysis–related article is a stub.You can help Wikipedia by expanding it.This hyperbolic geometry-related article is a stub.You can help Wikipedia by expanding it.

mathematicalfunctional analysisvector spaceconvergent sequencesreal numberscomplex numbersuniform normBanach spaceclosedlinear subspacespace of bounded sequences ℓ ∞ {\displaystyle \ell ^{\infty }} reflexiveRiesz representation theoremordinalSequence spaceAsplundBanachBanach latticeGrothendieck HilbertInner product spacePolarization identityPolynomiallyL-semi-inner productStrictlyUniformlyUniformly smoothInjectiveProjectiveTensor productof Hilbert spacesBarrelledCompleteF-spaceFréchetLocally convexMinkowski functionalsMackeyMetrizableNormedQuasinormedStereotypeBanach–Mazur compactumDual spaceDual normOperatorUltraweakStrongUltrastrongUniform convergenceLinear operatorsAdjointBilinearsesquilinearBoundedCompacton Hilbert spacesContinuousDensely definedkernelHilbert–SchmidtFunctionalspositivePseudo-monotoneNormalNuclearSelf-adjointStrictly singularTrace classTransposeUnitaryOperator theoryBanach algebrasC*-algebrasOperator spaceSpectrumC*-algebraradiusSpectral theoryof ODEsSpectral theoremPolar decompositionSingular value decompositionAnderson–KadecBanach–AlaogluBanach–MazurBanach–SaksBanach–Schauder (open mapping)Banach–Steinhaus (Uniform boundedness)Bessel's inequalityCauchy–Schwarz inequalityClosed graphClosed rangeEberlein–ŠmulianFreudenthal spectralGelfand–MazurGelfand–NaimarkGoldstineHahn–Banachhyperplane separationKrein–MilmanMackey–ArensMazur's lemmaM. Riesz extensionParseval's identityRiesz's lemmaRiesz representationSchauder fixed-pointAbstract Wiener spaceBanach manifoldbundleBochner spaceConvex seriesDifferentiation in Fréchet spacesDerivativesGateauxfunctionalholomorphicIntegralsBochnerDunfordGelfand–PettisregulatedPaley–WienerFunctional calculusMeasuresLebesgueProjection-valuedVectorWeaklyStronglyAbsolutely convexAbsorbingAffineBalanced/CircledConvexConvex cone (subset)Linear cone (subset)RadialRadially convex/Star-shapedSymmetricZonotopeAffine hullAlgebraic interior (core)Bounding pointsConvex hullExtreme pointInteriorLinear spanMinkowski additionAbsolute continuity AC b a ( Σ ) {\displaystyle ba(\Sigma )} Banach coordinate BKBesov B p , q s ( R ) {\displaystyle B_{p,q}^{s}(\mathbb {R} )} Birnbaum–OrliczBounded variation BVBs spaceContinuous C(K) with K compact HausdorffHardy HpMorrey–Campanato L λ , p ( Ω ) {\displaystyle L^{\lambda ,p}(\Omega )} Schwartz S ( R n ) {\displaystyle S\left(\mathbb {R} ^{n}\right)} Segal–Bargmann FSobolev Wk,pSobolev inequalityTriebel–LizorkinWiener amalgam W ( X , L p ) {\displaystyle W(X,L^{p})} Differential operatorFinite element methodMathematical formulation of quantum mechanicsOrdinary Differential Equations (ODEs)Validated numericstopicsglossaryHölderOrliczSchwartzSobolevTopological vectorSeparableUniform boundedness principleMin–maxUnboundedBanach algebraSpectrum of a C*-algebraOperator algebraGroup algebra of a locally compact groupVon Neumann algebraInvariant subspace problemMahler's conjectureHardy spaceSpectral theory of ordinary differential equationsHeat kernelIndex theoremCalculus of variationsIntegral linear operatorJones polynomialTopological quantum field theoryNoncommutative geometry