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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.
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