TY - JOUR

T1 - On the essential spectrum of n-body hamiltonians with asymptotically homogeneous interactions

AU - Georgescu, Vladimir

AU - Nistor, Victor

N1 - Publisher Copyright:
© 2017. Theta. All rights reserved.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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 πγ, where Y ⊂ X is a subspace, πγ: 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).

AB - 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 πγ, where Y ⊂ X is a subspace, πγ: 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).

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U2 - 10.7900/jot.2016apr08.2115

DO - 10.7900/jot.2016apr08.2115

M3 - Article

AN - SCOPUS:85017515223

SN - 0379-4024

VL - 77

SP - 333

EP - 376

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -