A Sharp Kato-Rosenblum Type Theorem for Unbounded n-Tuples

Abstract

We prove a generalization for commuting $n$-tuples of unbounded self-adjoint operators and the Lorentz $(n,1)$ ideal,$n \ge 3$, of the Kato-Rosenblum theorem. The result is derived from earlier work for bounded operators [8]. Also, a very weak result for $n=2$ unbounded operators and other additional results are obtained.