Revision #492 → #1028 · back to history
addedBanach space8d3ff30d3808
addedNormed space7ac53cdabe25
addedNorm-induced (canonical) metric5feadb68f62f
addedCauchy sequence045cfc569922
addedComplete norm113579006268
addedExistence of L-semi-inner product9364390451e6
addedSeries characterization of completeness85a52baa11e4
addedNorm-induced topology485a0a2060a8
addedBanach space is a Baire spaced99fbd5127af
addedOpen and closed balls100db1d956f6
addedCompact ball iff finite-dimensional5afd2eee0573
addedFinite-dimensional spaces are separable Banach spaces4ef7e8845bdb
addedSeparable Hilbert space isometric to ℓ²2bb3e364f5ad
addedAnderson–Kadec theorem160c017f95bc
addedMetric Banach manifold62d8ffb54d6a
addedHenderson embedding theorem7cb52c2ba6b8
addedCompact set with non-closed convex hull0b15951071da
addedClosed convex hull of compact set is compactb45685d70162
addedTopological vector spacecb84261d8588
addedCharacterization of normable TVS554be8e61e83
addedBanach spaces are barrelled84bf898c3321
addedComparison of complete metrizable topologies3b9c42d77bf6
addedEquivalent norms727296f09afb
addedCompleteness under equivalent normsd422d71d46c7
addedAll norms equivalent in finite dimension28b566b3d676
addedWhen a metric is norm-induced229693937b1d
addedTranslation-invariant metric and completeness2c9cc69acaf7
addedKlee's theoremf27a45db5d5e
addedFréchet space584f313f8b4d
addedBanach spaces are Fréchet spaces48be31679590
addedComplete topological vector spaceda81100c2954
addedBanach iff complete as TVS435ae3c3fc82
addedNormability via strong dualc88ca5219e3a
addedCompletion of a normed space1e321f7c1ffa
addedUniqueness of completionee7701f6c0e6
addedContinuity iff bounded on unit ball2195e91b2748
addedL(X,Y) is a Banach space6410ef563cc1
addedL(X) is a unital Banach algebraedd5e8a05adb
addedIsomorphic normed spaces97359cf7072d
addedIsometrically isomorphic spaces1c483665e493
addedBanach–Mazur distance6e765038897b
addedBounded equals continuous for linear operators99a7c43d7cb8
addedContinuity of subadditive functions7dc8d0f51764
addedFunctional continuous iff real part is363868368b82
addedProduct complete iff factors completeee06b056f06a
addedQuotient norm94cc673390f1
addedQuotient is Banach when X complete820725f80250
addedComplemented subspace597931aa4603
addedCanonical factorization of bounded operator34e47a7278bd
addedClassical Banach spaces67b8d88f125c
addedBanach–Mazur theorem3c2226e8124f
addedHilbert space as Banach space0ef5268cbaf0
addedL² is a Hilbert space66c05241dcec
addedHardy and Sobolev spacesf88ce2e71c43
addedBanach algebraad5bbede7af4
addedC(X) with pointwise product059e5625385d
addedDisk algebrab9abe4dbc56e
addedWiener algebradf7f24d73c9d
addedBounded operators as Banach algebra78cdedef2530
addedC*-algebraeac21142e98b
addedGelfand–Naimark theorembe5ddf9637e1
addedContinuous dual spacead45d94c4874
addedDual is a Banach space770a25348505
addedHahn–Banach extension of functionalsaaa68e58fe6b
addedNorming functional9f0e77f190ab
addedHahn–Banach separation theorema701472eb3f4
addedTotal subsetfb460edd30ae
addedDual of a direct sum046704dd7cba
addedHahn–Banach theorem48180173bd2f
addedSeparability of dual implies separabilityfb767f0e4a8b
addedWeak topology15b87b3dcbff
addedNorm-closed convex sets are weakly closed6afd3dde22ab
addedNorm-continuous maps are weakly continuousc9c42fffb2b6
addedAlgebraic dual spaced596b4ba69a8
addedWeak* topologyffb1959b63f5
addedBanach–Alaoglu theorem70b18220a66c
addedDual of ℓ¹d10318465a11
addedDual of Lp spaceee1f9aad4fb1
addedRiesz representation theoremacf2cc57fdeb
addedDual of C(K) as Radon measures30b608b198e2
addedAmir–Cambern extension017cc54658ef
addedMaximal ideals as Dirac measuresc0f1b2195833
addedGelfand–Mazur identification of maximal idealsa51c96b5e96e
addedGelfand representation theorem555337f3261d
addedBanach–Stone theorem2233fdddc9c2
addedMaximal ideal space of C(X)a86a25d5c460
addedBidual (second dual)76958b8115d0
addedCanonical map into bidual is isometric30f2e894ce97
addedReflexive spaceabadacf744b2
addedReflexive normed spaces are Banach9f9b2eb53806
addedGoldstine theorem76f691be86ed
addedBanach space not a countable union of closed subspaces02c4926fd814
addedCountable Hamel basis implies finite-dimensional28bf1a52b1a9
addedBanach–Steinhaus theorem224e96ed8e67
addedOpen Mapping theoremf4a3f0d845ee
addedBounded bijection is an isomorphisma05796e23e58
addedFirst Isomorphism theorem for Banach spacesaef4e6a0f6e5
addedClosed Graph theorem4cf2cc871932
addedReflexive normed space719bc9426f62
addedReflexive normed spaces are Banach spacesba1fcea43035
addedBounded surjection preserves reflexivity326072f8374f
addedSeparable dual implies separable86d07197df8f
addedReflexive and non-reflexive spaces1fbf1545cc70
addedJames space73297e94cd9d
addedClosed bounded convex sets weakly compactaf7ad7348850
addedConvex functions attain minimum on unit ballcbb237d1100d
addedBishop–Phelps theorem782bee1ad686
addedSubspaces and quotients of reflexive spaces51adcaaf675a
addedX reflexive iff dual reflexive3d1c079dbdaa
addedReflexive separable iff dual separablec3f25502ae7f
addedProduct reflexive iff factors reflexive45dfcc82b729
addedReflexive iff unit ball weakly compactb6a1982a1512
addedJames' theorem567d5ee84f2f
addedWeakly convergent sequence6903f96e748d
addedWeakly Cauchy sequence728426826c2a
addedWeakly* convergent sequence44fa3da3a153
addedWeakly sequentially complete spacedba381ed766e
addedOrthonormal sequence converges weakly to zeroc5914f62e30d
addedConvex combinations of weakly null sequence norm-converged93ba65be78f
addedSchur property of ℓ¹a7cda983a53c
addedL¹(μ) is weakly sequentially complete99730ecd3b9c
addedUnit ball of bidual as first Baire class11802f917a3e
addedRosenthal ℓ¹ dichotomy theorembe899b6f16f1
addedOdell–Rosenthal characterizationf0e2bd02df70
addedSeparable space has weak*-compact metrizable dual ball9707ef2783dd
addedWeak topology metrizable iff finite-dimensional63a5ea1f64d0
addedReflexivity via bounded sequences1ed6905b1895
addedWeakly compact subset of ℓ¹ is norm-compact4d8ba2d1e78c
addedEberlein–Šmulian theoreme245229f0694
addedType and cotype6fcb1ba530d3
addedSchauder basis5869f1e05ad7
addedSchauder basis implies separable1740ea9a3d55
addedBiorthogonal functionalsa9bcbe9a27c5
addedClassical explicit bases543978a502f4
addedBočkarev basis for disk algebra47bc6e994715
addedBasis implies bounded approximation property9dce50b55dc8
addedEnflo space without approximation propertyf066a3aa0f5d
addedJames reflexivity criterion for bases59f34c9ca89d
addedTensor product and universal property1bef54bb4f97
addedUniversal property of tensor product91375021a0db
addedSimple tensor5f7b07f5db6a
addedProjective and injective cross norms334fb0cae3ff
addedProjective tensor producta640ed70b354
addedGrothendieck tensor isomorphisms8ccf81398b50
addedTensor product as closure of finite rank operatorscf8fc8c4758c
addedInjectivity criterion and approximation property353ddc3385e6
addedPisier disproof of Grothendieck conjecture9a4f3672fc04
addedSzankowski: B(H) lacks approximation property3490cda9ccb1
addedParallelogram identity characterizes inner productb0fe96949884
addedPolarization identity recovers inner product91895b80b8d7
addedKwapień's theorem2a174a69c9f1
addedLindenstrauss–Tzafriri complementation theorem268fd4b4a3ad
addedDvoretzky's theorem9451392998f8
addedHomogeneous Banach space398d7f506d13
addedHereditarily indecomposable spacebe1117a9533c
addedGowers dichotomy theorembe979709fc78
addedParallelogram identity4a3a07c81172
addedHomogeneous space is separable Hilbert2bfc57a11f89
addedMazur–Ulam theorem5864ce71ac2f
addedFinite-dimensional homeomorphism classification43a1525ca8ad
addedSeparable Banach spaces are homeomorphic2700d2047989
addedToruńczyk density character classification2735ee01faba
addedHomeomorphic compacta give isometric C(K)9b1f797f6dbb
addedCountable compacta as ordinal intervals576f8d46f3cc
addedMilutin theorem68286c917aba
addedFréchet derivative on Banach spaces9edad3709514
addedComplete non-Banach spaces8ffb9aa7db2b