For proper Banach algebra coefficients, the Bost assembly map is split surjective and the right-hand side of the conjecture does not depend on the choice of the unconditional completion involved. These results hold for a large class of unconditional completions.
Cite this article
Walther Paravicini, The Bost conjecture and proper Banach algebras . J. Noncommut. Geom. 7 (2013), no. 1, pp. 191–202DOI 10.4171/JNCG/113