A few results on Mourre theory in a two-Hilbert spaces setting

Details A few results on Mourre theory in a two-Hilbert spaces setting A few results on Mourre theory in a two-Hilbert spaces setting

2011-04-09

arxiv.org/abs/1104.1665v1

Physics

Mathematical Physics

13 pages

Scientific paper

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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