### Abstract

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 ε (X) be the algebra generated by functions of the form v o π_{γ}, where Y ⊂ X is a subspace, π_{γ}: X → X/Y is the projection, and v: X/Y → C is continuous with uniform radial limits at infinity. We consider Hamiltonians affiliated to ε(X) := ε (X) × X. We determine the characters of ε (X) and then we describe the quotient of ε(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 ε (X).

Original language | English (US) |
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Pages (from-to) | 333-376 |

Number of pages | 44 |

Journal | Journal of Operator Theory |

Volume | 77 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2017 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

*Journal of Operator Theory*,

*77*(2), 333-376. https://doi.org/10.7900/jot.2016apr08.2115