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October 13, 2018 By

Uniqueness of the Index Map in Banach Algebra K-theory, II

C. R. Math. Rep. Acad. Sci. Canada Vol. 40 (3) 2018, pp. 91-100

September 30, 2018

George A. Elliott,Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4; e-mail: elliott@math.toronto.edu

Abstract/Résumé:

It is shown that the index map in the theory of real Banach algebras is unique as a natural transformation, up to an integral multiple, and modulo a (unique) two-torsion “ghost” map arising from the order-two K\(_1\)-group of the Banach algebra \({\mathbb R}\) (of real numbers). (In the earlier paper this was shown for complex Banach algebras, of course without the “ghost” map, but in way—using Bott periodicity to pass to the opposite parity—that is not available for real Banach algebras. The present approach yields a new proof in the complex case.)

On démontre que l’application index dans la K-théorie des algèbres de Banach réelles (ou complexes) est essentiellment unique.

Keywords: K-theory, index theory
AMS Subject Classification: Index theory, K-theory and operator algebras -including cyclic theory 19K56, 46L80

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