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

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Abstract

We consider a closed densely defined linear operatorT in a Hilbert spaceE, and assume the existence ofξ 0 ∈ϱ(T) such thatK = (T -ξ 0 I)-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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Authors and Affiliations

  1. Département de Mathématiques, Université de Provence, Place V. Hugo, F-13331, Marseille Cedex 3, France

    Marie Thérèse Aimar

  2. Département de Mathématiques, Université de Corte, Quartier Grossetti, F-20250, Corte, France

    Abdelkader Intissar & Jean Martin Paoli

Authors
  1. Marie Thérèse Aimar
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  2. Abdelkader Intissar
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  3. Jean Martin Paoli
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Communicated by H. Araki

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Aimar, M.T., Intissar, A. & Paoli, J.M. Densité des vecteurs propres généralisés d'une classe d'opérateurs compacts non auto-adjoints et applications. Commun.Math. Phys. 156, 169–177 (1993). https://doi.org/10.1007/BF02096736

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  • DOI: https://doi.org/10.1007/BF02096736

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