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# Operator Algebra and Noncommutative Geometry Seminar Series

## August 2, 2018 @ 3:30 pm - 4:30 pm

##### Title

Sums of linear operators in Hilbert C*-modules

##### Speaker

Professor Matthias Lesch ( der Universität Bonn)

##### Abstract

Given two closed unbounded operators A, B in a Banach space. There is a rich literature on the problem whether the sum A+B is closed and regular on the intersection of the domains $D_A \cap D_B$. The seminal paper by da Prato and Grisvard (1975) and its successors are mostly motivated by applications to PDE.

Another completely different and quite recent motivation comes from the unbounded picture of KK-theory. Here, one typically encounters pairs of *weakly anticommuting* self-adjoint operators acting on a Hilbert C*-module.

In my talk, I will present a Hilbert C*-module version of a noncommutative Dore-Venni type Theorem for noncommuting operators. This will generalize previous work on weakly anticommuting operators arising from Kasparov products.