Abstract
The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C∗C∗-module is isomorphic to a direct summand in the standard module of square summable sequences in the base C∗C∗-algebra. In this paper, this result will be generalized by incorporating a densely defined derivation on the base C∗C∗-algebra. This leads to a differentiable version of the Kasparov absorption theorem. The extra compatibility assumptions needed are minimal: It will only be required that there exists a sequence of generators with mutual inner products in the domain of the derivation. The differentiable absorption theorem is then applied to construct densely defined connections (or correpondences) on Hilbert C∗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∗C∗-module.
Original language | English |
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Journal | Journal of Noncommutative Geometry |
Volume | 11 |
Issue number | 3 |
Pages (from-to) | 1037-1068 |
ISSN | 1661-6952 |
DOIs | |
Publication status | Published - 2017 |
Keywords
- Hilbert C∗C∗-modules
- derivations
- differentiable absorption
- Grassmann connections
- regular unbounded operators
- Regular unbounded operators
- Derivations
- Graßmann connections
- Hilbert C∗-modules
- Differentiable absorption