The Birman-Schwinger principle in von Neumann algebras of finite type
Vadim Kostrykin, Konstantin A. Makarov, Anna Skripka
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.
Create a lesson
Related papers
Spectra of Non-Self-Adjoint Almost Mathieu Matrices and the Scottish Flag Operator
Simon Becker, Izak Oltman
Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
Zhongkai Tao, Mengxuan Yang
Uniform Non-Localization for Laplace Eigenfunctions on the Equilateral Triangle: Dirichlet, Neumann, and Robin Boundary Conditions
Binh T. Nguyen
Scaling inequalities and limits for clamped plate eigenvalues on geodesic disks
Scott Harman
Non-Elliptic Quadratic PT-Symmetric Operators and Similarity to Self-Adjoint Operators
Stepan Malkov
Complex Analysis in completeness, spectral and scattering problems
Alexei Poltoratski