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

Vadim Kostrykin; Konstantin A. Makarov; Anna Skripka

doi:10.1016/j.jfa.2006.12.001

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

Vadim Kostrykin·Konstantin A. Makarov·Anna Skripka

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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.

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BibTeX RIS

Vadim Kostrykin, Konstantin A. Makarov, Anna Skripka. 2006-10-09. The Birman-Schwinger principle in von Neumann algebras of finite type. https://doi.org/10.1016/j.jfa.2006.12.001

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