A few results on Mourre theory in a two-Hilbert spaces setting
Résumé
We introduce a natural framework for dealing with Mourre theory in an abstract two-Hilbert spaces setting. In particular a Mourre estimate for a pair of self-adjoint operators $(H,A)$ is deduced from a similar estimate for a pair of self-adjoint operators $(H_0,A_0)$ acting in an auxiliary Hilbert space. A new criterion for the completeness of the wave operators in a two-Hilbert spaces setting is also presented.
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