Journal of Operator Theory

Volume 55, Issue 2, Spring 2006 pp. 253-268.

On the spectral theory of tensor product Hamiltonians

Authors: Mondher Damak
Author institution: Department of Mathematics, Faculty of Sciences of Sfax, B.P. 802, Sfax, 3018, Tunisia

Summary: We develop, in this paper the Mourre theory for an abstract class of self-adjoint operators of the form $H_1 \otimes I + I \otimes H_2$, where $H_1$ and $H_2$ are two self-adjoint operators acting on the Hilbert spaces $\mathcal H_1$ and $\mathcal H_2$ respectively. $H_1$ and $H_2$ do not need to be lower semi-bounded. As an example, we consider the time periodic Hamiltonians for which we construct a conjugate operator, prove a Mourre estimate and, finally, study some of its perturbations.

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