English

Essential spectrum of a limit of self--adjoint operators

Mathematical Physics 2012-08-28 v2 math.MP

Abstract

For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.

Keywords

Cite

@article{arxiv.1208.4686,
  title  = {Essential spectrum of a limit of self--adjoint operators},
  author = {Dmitry K. Gridnev},
  journal= {arXiv preprint arXiv:1208.4686},
  year   = {2012}
}

Comments

The paper has been withdrawn due to a wrong example concerning compact operators. Furthermore, the proof in Weidmann's back appears to be correct. With thanks to F. Gesztesy and Gerhard Teschl