### Resumé

Originalsprog | Engelsk |
---|---|

Tidsskrift | Journal of Noncommutative Geometry |

Vol/bind | 11 |

Udgave nummer | 3 |

Sider (fra-til) | 1037-1068 |

ISSN | 1661-6952 |

DOI | |

Status | Udgivet - 2017 |

### Fingeraftryk

### Citer dette

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*Journal of Noncommutative Geometry*, bind 11, nr. 3, s. 1037-1068. https://doi.org/10.4171/JNCG/11-3-8

**Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators.** / Kaad, Jens.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators

AU - Kaad, Jens

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Hilbert C∗C∗-modules

KW - derivations

KW - differentiable absorption

KW - Grassmann connections

KW - regular unbounded operators

U2 - 10.4171/JNCG/11-3-8

DO - 10.4171/JNCG/11-3-8

M3 - Journal article

VL - 11

SP - 1037

EP - 1068

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 3

ER -