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Search: MSC category 47A40 ( Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx] )

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1. CMB 2004 (vol 47 pp. 144)

Xia, Jingbo
On the Uniqueness of Wave Operators Associated With Non-Trace Class Perturbations
Voiculescu has previously established the uniqueness of the wave operator for the problem of $\mathcal{C}^{(0)}$-perturbation of commuting tuples of self-adjoint operators in the case where the norm ideal $\mathcal{C}$ has the property $\lim_{n\rightarrow\infty} n^{-1/2}\|P_n\|_{\mathcal{C}}=0$, where $\{P_n\}$ is any sequence of orthogonal projections with $\rank(P_n)=n$. 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 uniqueness in the case of trace-class perturbation.)

Categories:47A40, 47B10

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