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

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

2006-10-09

arxiv.org/abs/math/0610282v1

J. Funct. Anal. 247 (2007), 492 - 508

Mathematics

Spectral Theory

Scientific paper

10.1016/j.jfa.2006.12.001

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.

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