
Speaker: 
Jens Kaad (SISSA, Trieste)

Title: 
Differentiable absorption of Hilbert \(C^*\)modules

Abstract: 
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.

