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Takesaki, Masamichi

Theory of operator algebras I. (English) Zbl 0436.46043

New York, Heidelberg, Berlin: Springer-Verlag. VII, 415 p. DM 79.00; $ 44.30 (1979).
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scan of Zbl 0436.46043

Cited in 10 Reviews
Cited in 701 Documents

MathOverflow Questions:

Name for a set of elements that fully determine a morphism

MSC:

46L05 General theory of \(C^*\)-algebras
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
46L10 General theory of von Neumann algebras
46L35 Classifications of \(C^*\)-algebras
46L45 Decomposition theory for \(C^*\)-algebras
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras

Keywords:

Gelfand representation; automatic continuity; cone of positive elements; bounded approximate unit; Gelfand-Naimark-Segal construction; asymmetric Riesz decomposition; von Neumann’s locally convex operator topologies; double commutant; predual; Kaplansky’s density theorem; Kadison’s transitivity theorem; non-commutative analogues of Lusin’s and Egorov’s theorems; universal enveloping von Neumann algebra; polar decomposition of functionals; Arens-Mackey topology; universal measurability; completely positive maps; Tomita’s commutant theorem; direct integrals; desintegration of von Neumann algebras; Murray-von Neumann dimension theory; multiplicities; factors; maximal ideal space
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