Titlebook: Combinatorial Set Theory of C*-algebras; Ilijas Farah Book 2019 Springer Nature Switzerland AG 2019 C*-algebras.Calkin algebra.combinatori

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The Calkin Algebranuum Hypothesis is used to construct nondiagonalizable pure states on ., refuting a conjecture of Anderson and giving a negative answer to a problem of Kadison and Singer; this is a theorem of Akemann and Weaver. We offer additional proofs of this theorem from two weakenings of the Continuum Hypothe

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Degree-1 Saturationt every uniformly bounded representation of a countable amenable group into such C.-algebra is unitarizable (Section 15.4.1; this fails for uncountable groups, Section .), and that such C.-algebras admit a poor man’s version of Borel functional calculus that generalizes the Brown–Douglas–Fillmore “S

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