Trieste, August 26-28 2014

K-homology and graph algebras

Differentiable absorption of Hilbert C*-modules

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C*-module is isomorphic to a direct summand in a standard module. In this talk, I will generalize this result by incorporating a densely defined derivation on the base C*-algebra. The extra compatibility assumptions needed are minimal: It will only be required that there exists a sequence of generators with inner products in the domain of the derivation. As an application, I will show how to construct densely defined connections (or correspondences) on Hilbert C*-modules. These connections can in turn be used to define selfadjoint and regular "lifts" of unbounded operators which act on an auxiliary Hilbert C*-module.