Abstract
Around 1978 Max Karoubi made a striking conjecture about the K-theory of Banach algebras. His conjecture predicted that the topological K-groups K * top(B) of a unital Banach algebra B were isomorphic to the algebraic K-groups K *(B⊗r)C) of the Grothendieck’s projective tensor product of B and the ideal K of compact operators on the standard Hilbert space H = ℓ2 (ℕ). Notice that B⊗K, is a norm completion of the matrix algebra M ∞(B) = B ⊗ M ∞(ℂ) and K *(M ∞(B)) = K *(B).
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© 1994 Birkhäuser Verlag
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Wodzicki, M. (1994). Algebraic K-Theory and Functional Analysis. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992. Progress in Mathematics, vol 120. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9112-7_22
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DOI: https://doi.org/10.1007/978-3-0348-9112-7_22
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