2021/09/09 by Qihui Li, Rui Wang, Li, Qihui +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2109.04135
openalex publication_date 2021/09/09 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28
Let M be a countable decomposable properly infinite semifinite von Neumann algebra acting on a Hilbert space H. An analogue of the Kato-Rosenblum theorem in M has been proved in [9] by showing the existence of generalized wave operators. It is well-known that there are two typical approaches to show the existence of wave operators in the scattering theory. One is called time-dependent approach and another is called stationary approach. The main purpose of this article is to introduce a stationary approach in M and then to obtain the Kato-Rosenblum theorem in M by a stationary approach instead of a time-dependent approach in [9].