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All nuclear C*-algebras are amenable. (English) Zbl 0529.46041


MSC:

46L05 General theory of \(C^*\)-algebras
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47B47 Commutators, derivations, elementary operators, etc.
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References:

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[12] de la Harpe, P.: Moyennabilité du groupe unitaire et propriété P de Schwartz des algèbres de von Neumann. Lecture notes in Mathematics, vol. 725, pp. 220-227. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0402.46037
[13] Johnson, B.E.: Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127 (1972) · Zbl 0256.18014
[14] Johnson, B.E.: Approximate diagonals and cohomology of certain annihilator Banach algebras. Amer. J. Math.94, 685-698 (1972) · Zbl 0246.46040 · doi:10.2307/2373751
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[16] Pisier, G.: Grothendieck’s Theorem for non commutativeC *-algebras with an appendix on Grothendieck’s constant. J. Funct. Analysis29, 397-415 (1978) · Zbl 0388.46043 · doi:10.1016/0022-1236(78)90038-1
[17] Ringrose, J.R.: Automatic continuity of derivations of operator algebras. J. London Math. Soc.5, 432-438 (1972) · Zbl 0245.46084 · doi:10.1112/jlms/s2-5.3.432
[18] Rosenberg, J.: Amenability of crossed products ofC *-algebras. Commun. Math. Phys.57, 187-191 (1977) · Zbl 0399.46046 · doi:10.1007/BF01625777
[19] Takesaki, M.: Theory of operator algebras I. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0436.46043
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