Generalized Wave Operators in von Neumann Algebras

Abstract

Let $\mathcal{M}\subseteq \mathcal{B}\left(\mathcal{H}\right)$ be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight $\tau$ where $\mathcal{B}\left(\mathcal{H}\right)$ is the set of all bounded linear operators on Hilbert space $\mathcal{H}.$ The main purpose of this article is to introduce generalized weak wave operators ${\tilde{W}}_{\pm }$, generalized weak abelian wave operators ${\tilde{\mathfrak{U}}}_{\pm }$ and generalized stationary wave operators ${\mathcal{U}}_{\pm }$ in $\mathcal{M}$ and then to explore the relation among ${\tilde{W}}_{\pm },$ $\widetilde{\mathfrak{U}% }_{\pm}$, ${\mathcal{U}}_{\pm }$ and generalized wave operators $W_{\pm }.$

We combine this paper with paper arXiv:2109.04135

Cited by in corpus (1)

• A stationary approach for the Kato-Rosenblum theorem in von Neumann algebras