Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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. https://doi.org/10.1215/17358787-3163312

Information

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

Subjects:
Primary: 46L05, 46L80, 46L87

Rights: Copyright © 2016 Tusi Mathematical Research Group

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.10 • No. 1 • January 2016
Back to Top