Revision #350 → #1657 · back to history
addedVon Neumann algebra (W*-algebra)ccbd172f7574
addedDouble commutant theorem (informal)4cc8de3ddb54
addedEssentially bounded functions on the real line324b64fbe17b
addedAll bounded operators on a Hilbert spaceaa4404fd0f0b
addedFirst definition: weakly closed *-algebraff5321cf3ce0
addedNorm-closed *-algebras are C*-algebras782258e9f762
addedSecond definition: double commutantdd1194412832
addedVon Neumann double commutant theoremde24babf988e
addedAbstract definition via predual760eaae499f5
addedUniqueness of the predualf3ba3d86d033
addedFinite von Neumann algebra21ab29cc9b96
addedProperly infinite von Neumann algebra5284a2b1fcc7
addedSeparable von Neumann algebra988db7abec4d
addedGenerated von Neumann algebra174a12db4172
addedTensor product of von Neumann algebras46181fd2d42a
addedVon Neumann algebras are semihereditary46772488ad4e
addedAffiliated operators form a von Neumann regular ringfe0c8c0465a4
addedClassification of commutative von Neumann algebras2146a647b29e
addedProjectionfb3e7dba8f7e
addedSubspace belonging to M8bf6ac1a5356
added1:1 correspondence projections/subspaces96fc100b5b81
addedClosures of images and kernels belong to M3cf44ee58bf9
addedMurray–von Neumann equivalencefd1b2ecac53e
addedAdditivity of equivalence99811213cf83
addedSchröder–Bernstein theorem for operator algebras5cd11c332613
addedTotal order on equivalence classes in a factor9ecc13106eb3
addedFinite projection55abb398a361
addedVon Neumann algebra generated by projectionsb163cf22300b
addedProjections of a finite factor form a continuous geometryc0fbfff9de4a
addedFactor (center is scalar multiples)a3f3a883e5a0
addedDirect integral decomposition into factors215730005001
addedEvery factor has one of three types6b007f635265
addedUnique decomposition into types I, II, III33af5609785b
addedDiscrete and continuous factors5fd294fb0275
addedSemifinite and purely infinite factors9dd6f5788f1d
addedFinite and properly infinite factors41784214250e
addedType I factorbf1eb0430eef
addedType I factors are B(H)e3a35b5369ce
addedType II factor7520b54db7c6
addedType II_1 and II_∞65424503e147
addedUniqueness of hyperfinite type II factors318a2b0b9686
addedUnique tracial state on a type II_1 factoraeed2b59b7e6
addedSemifinite trace on type II_∞ factord2fb5b44425f
addedFundamental group of a type II_∞ factorfa819c73c6dd
addedTensor product yields type II_∞ff8145c6acb6
addedFundamental group of a type II_1 factor412460d0b7d6
addedConnes: property (T) gives countable fundamental group07d29d04c241
addedPopa: trivial fundamental group2892750ad477
addedType II_1 group von Neumann algebra (ICC group)56a8381b597c
addedMcDuff: uncountably many type II_1 factors97860e9fc289
addedType III factor172d952641b8
addedType III_λ via Connes spectrumab4050dc3cea
addedTrace and projections on type III factorsac7ae00afa06
addedType III as crossed product (Tomita–Takesaki)27ac3ac5ebae
addedM is the dual of its predual0199bfbc5954
addedUniqueness of the predual052aaf083fd3
addedSakai: predual characterizes von Neumann algebras8abb466cef48
addedPredual is a proper closed subspace of the dual87d96e6f64e1
addedPredual of L∞(R) is L1(R)992ab850b236
addedPredual of B(H) is trace class operators9e1a0b00e69b
addedPredual of VN(G) is the Fourier algebra7d6ef551162d
addedPositive linear functional10183d143ac8
addedTracial state8f846baec4a3
addedUnique trace on a factor9238b98700b0
addedNormal state from a unit vector (GNS)c325b9da7f96
addedClassification of modules by M-dimension2945f9635376
addedStandard modulecba67a9ab0d7
addedExistence and uniqueness of standard representation866c0e1c4863
addedEquivalent characterizations of amenability845d3dd71beb
addedClassification of amenable factors9308264ebae6
addedAmenable factors via group-measure space constructionddded18faba0
addedFiniteness of tensor products785c8cef665b
addedType of a tensor product is the maximumff21b2d2d6f9
addedCommutation theorem for tensor productsf6accb712777
addedInfinite tensor product via states412b6c3d4665
addedAraki–Woods (ITPFI) factorse33dc71884cc
addedPowers factors405a5a6049c4
addedHyperfinite (not III_0) factors are Araki–Woods5ab96d128be2
addedBimodule (correspondence)6e5fcfbfe4f3
addedBimodules yield subfactorsadcf54e0e9fa
addedVoiculescu: disjointness of non-amenable factor classes4c235c817424
addedOzawa: hyperbolic groups give prime II_1 factors3730f106c6d0
addedEssentially bounded functions on a σ-finite measure space94c5774175d5
addedKaplansky density theoremd860affd16ee
addedBounded operators on a Hilbert space (type I factor)465511d7f52f
addedCommutant of a unitary group representationdbe5e124ca55
addedVon Neumann group algebra of a discrete groupb1459ff8b4c3
addedTensor product as a von Neumann algebra8099e7debcdf
addedCrossed product by a groupf0f77e89cd6e
addedVon Neumann algebras of equivalence relations and groupoids4b2e32e2e680