Communications in Mathematical Physics

, Volume 30, Issue 1, pp 23–34 | Cite as

Essential self-adjointness of operators in ordered hilbert space

  • William G. Faris


LetH0≧0 be a self-adjoint operator acting in a spaceL2(M, μ). It is assumed thatH0e=0, wheree is strictly positive, and that exp(−tH0) is positivity preserving fort≧0. LetV be a real function onM such that its positive part is inL2(M,e2μ) and its negative part is relatively small with respect toH0. ThenH=H0+V is essentially self-adjoint on the intersection of the domains ofH0 andV. This result is applied to Schrödinger operators and to quantum field Hamiltonians.


Neural Network Statistical Physic Hilbert Space Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • William G. Faris
    • 1
  1. 1.Battelle, Advanced Studies CenterGenevaSwitzerland

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