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arXiv · 1407.1389

Differentiable absorption of Hilbert C*-modules, connections, and lifts of unbounded operators

Jens Kaad
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Abstract

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C*-module is isomorphic to a direct summand in the standard module of square summable sequences in the base C*-algebra. In this paper, this result will be generalized by incorporating a densely defined derivation on the base 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 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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Jens Kaad. 2014-07-05. Differentiable absorption of Hilbert C*-modules, connections, and lifts of unbounded operators. https://arxiv.org/abs/1407.1389

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