ON THE ESSENTIAL SPECTRUM OF N-BODY HAMILTONIANS WITH ASYMPTOTICALLY HOMOGENEOUS INTERACTIONS

We determine the essential spectrum of Hamiltonians with N-body type interactions that have radial limits at infinity, which extends the classical HVZ-theorem for potentials that tend to zero at infinity. Let E(X) be the algebra generated by functions of the form v ○ π Y, where Y ⊂ X is a subspace,...

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Bibliographic Details
Published in:Journal of operator theory 2017-03, Vol.77 (2), p.333-376
Main Authors: GEORGESCU, VLADIMIR, NISTOR, VICTOR
Format: Article
Language:English
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Summary:We determine the essential spectrum of Hamiltonians with N-body type interactions that have radial limits at infinity, which extends the classical HVZ-theorem for potentials that tend to zero at infinity. Let E(X) be the algebra generated by functions of the form v ○ π Y, where Y ⊂ X is a subspace, π Y : X → X/Y is the projection, and v : X/Y → C is continuous with uniform radial limits at infinity. We consider Hamiltonians affiliated to E(X) := E(X) ⋊ X. We determine the characters of E(X) and then we describe the quotient of E(X)/K with respect to the ideal of compact operators, which in turn gives a formula for the essential spectrum of any self-adjoint operator affiliated to E(X).
ISSN:0379-4024
1841-7744
DOI:10.7900/jot.2016apr08.2115