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

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Abstract

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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Authors and Affiliations

  1. CNRS, UMR5208, Institut Camille Jordan, Université Lyon 1, Université de Lyon, 43 blvd du 11 novembre 1918, 69622 , Villeurbanne-Cedex, France

    S. Richard

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna, 4860 , Santiago, Chile

    R. Tiedra de Aldecoa

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  1. S. Richard
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  2. R. Tiedra de Aldecoa
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Correspondence to S. Richard.

Additional information

This work has been done while S. Richard was staying in Tsukuba (Japan). This stay was supported by the Japan Society for the Promotion of Science (JSPS) and by “Grants-in-Aid for Scientific Research”. R. Tiedra de Aldecoa was supported by the Fondecyt Grant 1090008 and by the Iniciativa Cientifica Milenio ICM P07-027-F “Mathematical Theory of Quantum and Classical Magnetic Systems”.

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Richard, S., Tiedra de Aldecoa, R. A few results on Mourre theory in a two-Hilbert spaces setting. Anal.Math.Phys. 3, 183–200 (2013). https://doi.org/10.1007/s13324-013-0055-8

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  • DOI: https://doi.org/10.1007/s13324-013-0055-8

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