Trace Class Methods

Abstract

In this section we want to derive the existence of strong wave operators under the assumption that HJ − JH ₀ is a trace operator. In the next section this result is used to obtain further useful statements on trace class perturbations of more general kind. The proof of the following theorem needs only the well-known Rosenblum lemma on Hilbert-Schmidt operators (see Prop. 3.24) and the fact that for compact operators C the expression C e⁻ⁱ tH ₀ P ^ac ₀ converges strongly to zero as t → ±∞. Further recall the concept of admissible functions (cf. Definition 8.16).