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Applied Categorical Structures

, Volume 25, Issue 5, pp 893–905 | Cite as

Atiyah-Jänich Theorem for σ-C*-algebras

  • Kamran SharifiEmail author
Article
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Abstract

K-theory for σ-C*-algebras (countable inverse limits of C*-algebras) has been investigated by N. C. Phillips (K-Theory 3, 441–478, 1989). We use his representable K-theory to show that the space of Fredholm modular operators with coefficients in an arbitrary unital σ-C*-algebra A, represents the functor X↦RK0(C(X,A)) from the category of countably compactly generated spaces to the category of abelian groups.

Keywords

Representable K-theory Inverse limit σ-C*-algebras Milnor \(\lim ^{1}\) exact sequence Fredholm operators Hilbert modules 

Mathematics Subject Classification (2010)

Primary 46L80 Secondary 19K35 46M20 46L08 
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Authors and Affiliations

  1. 1.Department of MathematicsShahrood University of TechnologyShahroodIran

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