Geodesic
On the Uniqueness of Wave Operators Associated with Non-Trace Class Perturbations
Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 144-151

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DOI

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 ${{\lim }_{n\,\to \,\infty }}\,{{n}^{-1/2}}\,\left\| {{P}_{n}} \right\|\mathcal{C}\,=\,0$ , 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.)
DOI : 10.4153/CMB-2004-015-4
Mots-clés : 47A40, 47B10 
Xia, Jingbo. On the Uniqueness of Wave Operators Associated with Non-Trace Class Perturbations. Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 144-151. doi: 10.4153/CMB-2004-015-4
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     journal = {Canadian mathematical bulletin},
     pages = {144--151},
     year = {2004},
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     doi = {10.4153/CMB-2004-015-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-015-4/}
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