On the Uniqueness of Wave Operators Associated With Non-Trace Class Perturbations

[摘要] Voiculescu has previously established the uniqueness of the wave operatorfor the problem of $mathcal{C}^{(0)}$-perturbation of commuting tuplesof self-adjoint operators in the case where the norm ideal $mathcal{C}$has the property $lim_{nightarrowinfty} n^{-1/2}|P_n|_{mathcal{C}}=0$,where ${P_n}$ is any sequence of orthogonal projections with $ank(P_n)=n$.We prove that the same uniqueness result holds true so long as $mathcal{C}$is not the trace class. (It is well known that there is no such uniquenessin the case of trace-class perturbation.)

[学科分类] 数学（综合）

[关键词] deformations;embeddability;complex ellipsoids