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January 2016 Pictures of KK-theory for real C-algebras and almost commuting matrices
Jeffrey L. Boersema, Terry A. Loring, Efren Ruiz
Banach J. Math. Anal. 10(1): 27-47 (January 2016). DOI: 10.1215/17358787-3163312


We give a systematic account of the various pictures of KK-theory for real C-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of KK-theory, and we use CRT-structures to prove that a natural transformation F(A)G(A) between homotopy equivalent, stable, half-exact functors defined on real C-algebras is an isomorphism, provided it is an isomorphism on the smaller class of C-algebras. Finally, we develop E-theory for real C-algebras and use that to obtain new negative results regarding the problem of approximating almost commuting real matrices by exactly commuting real matrices.


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Jeffrey L. Boersema. Terry A. Loring. Efren Ruiz. "Pictures of KK-theory for real C-algebras and almost commuting matrices." Banach J. Math. Anal. 10 (1) 27 - 47, January 2016.


Received: 24 March 2015; Accepted: 6 April 2015; Published: January 2016
First available in Project Euclid: 15 October 2015

zbMATH: 1352.46064
MathSciNet: MR3453522
Digital Object Identifier: 10.1215/17358787-3163312

Primary: 46L05, 46L80, 46L87

Rights: Copyright © 2016 Tusi Mathematical Research Group


Vol.10 • No. 1 • January 2016
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