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

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 d...

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Bibliographic Details
Published in:	Journal of functional analysis Vol. 247; no. 2; pp. 492 - 508
Main Authors:	Kostrykin, Vadim, Makarov, Konstantin A., Skripka, Anna
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15-06-2007
Subjects:	Dissipative operators Perturbation theory Von Neumann algebras Perturbation theory Von Neumann algebras Dissipative operators
Online Access:	Get full text
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Summary:	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.
ISSN:	0022-1236 1096-0783
DOI:	10.1016/j.jfa.2006.12.001