paper

The Birman-Schwinger principle in von Neumann algebras of finite type

arXiv:math/0610282 · doi:10.1016/j.jfa.2006.12.001

Abstract

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the algebra in terms of the relative index.

The Birman-Schwinger principle in von Neumann algebras of finite type · wovepaper