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Communications in Mathematical Physics

, Volume 156, Issue 1, pp 169–177 | Cite as

Densité des vecteurs propres généralisés d'une classe d'opérateurs compacts non auto-adjoints et applications

  • Marie Thérèse Aimar
  • Abdelkader Intissar
  • Jean Martin Paoli
Article

Abstract

We consider a closed densely defined linear operatorT in a Hilbert spaceE, and assume the existence ofξ0ϱ(T) such thatK = (T -ξ0I)-1 is compact and the existence ofp>0 such thats n (K)=o((n−1/p)), whereS n (K) denotes the sequence of non-zero eigenvalues of the compact hermitian operator\(\sqrt {K*K} \). In this work, sufficient conditions (announced in [1]) are introduced to assure that the closed subspace ofE spanned by the generalized eigenvectors ofT coincides withE. These conditions are in particular verified by a family of non-self-adjoint operators arising in reggeon's field theory.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Marie Thérèse Aimar
    • 1
  • Abdelkader Intissar
    • 2
  • Jean Martin Paoli
    • 2
  1. 1.Département de MathématiquesUniversité de ProvenceMarseille Cedex 3France
  2. 2.Département de MathématiquesUniversité de CorteCorteFrance

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