Atiyah-J\"anich theorem for $\sigma$-C*-algebras
Kamran Sharifi

TL;DR
This paper extends the Atiyah-Jänich theorem to $\sigma$-C*-algebras, showing that the space of Fredholm modular operators with coefficients in such algebras represents a specific K-theory functor.
Contribution
It demonstrates that the space of Fredholm modular operators for $\sigma$-C*-algebras represents the representable K-theory functor, generalizing classical results to a broader algebraic context.
Findings
The space of Fredholm modular operators represents the K-theory functor for $\sigma$-C*-algebras.
The result applies to countably compactly generated spaces.
It generalizes the Atiyah-Jänich theorem to $\sigma$-C*-algebras.
Abstract
K-theory for -C*-algebras (countable inverse limits of C*-algebras) has been investigated by N. C. Phillips [{\it K-Theory} {\bf 3} (1989), 441--478]. We use his representable K-theory to show that the space of Fredholm modular operators with coefficients in an arbitrary unital -C*-algebra , represents the functor from the category of countably compactly generated spaces to the category of abelian groups.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Mathematical Analysis and Transform Methods
