Vol. 3, No. 4, 2018

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Localization $C^*$-algebras and $K\mkern-2mu$-theoretic duality

Marius Dadarlat, Rufus Willett and Jianchao Wu

Vol. 3 (2018), No. 4, 615–630
Abstract

Based on the localization algebras of Yu, and their subsequent analysis by Qiao and Roe, we give a new picture of KK-theory in terms of time-parametrized families of (locally) compact operators that asymptotically commute with appropriate representations.

Keywords
K-theory, duality, operator algebras
Mathematical Subject Classification 2010
Primary: 19K35, 19K56
Secondary: 46L80
Milestones
Received: 21 September 2016
Revised: 27 February 2018
Accepted: 26 March 2018
Published: 18 December 2018
Authors
Marius Dadarlat
Department of Mathematics
Purdue University
West Lafayette, IN
United States
Rufus Willett
Department of Mathematics
University of Hawai‘i at Mānoa
Honolulu, HI
United States
Jianchao Wu
Department of Mathematics
Pennsylvania State University
University Park, PA
United States