Algebraic K-theory of stable C*-algebras

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Abstract

Let A be a unital C*-algebra and let l denote the Calkin algebra (the bounded operators on a separable Hilbert space, modulo the compact operators K). We prove the following conjecture of M. Karoubi: the algebraic and topological K-theory groups of the tensor product C*-algebra A ⊗ l are equal. The algebra A ⊗ l may be regarded as a "suspension" of the more elementary C*-algebra A ⊗ K; thus Karoubi's conjecture asserts, roughly speaking, that the algebraic and topological K-theories of stable C*-algebras agree.

Original languageEnglish (US)
Pages (from-to)1-140
Number of pages140
JournalAdvances in Mathematics
Volume67
Issue number1
DOIs
StatePublished - Jan 1988

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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