The Duality of Spectral Manifolds and Local Spectral Theory

  • V. Lomonosov
  • Yu. Lyubich
  • V. Matsaev
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)


Let T be an arbitrary linear bounded operator on a complex Banach space B. As usual, we denote by ρ(T) the resolvent set of T, i.e., ρ(T) is the set of λ ∈ C such that the resolvent R λ(T) = (T - λI)y-1 exists in the algebra of all linear bounded operators on B. This set is open and R λ(T) is an analytic operator function on it. The spectrum σ(T) = C/ρ(T) is compact.


Linear Subspace Complex Banach Space Linear Continuous Functional Spectral Subspace Invariant Closed Subspace 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • V. Lomonosov
    • 1
  • Yu. Lyubich
    • 2
  • V. Matsaev
    • 3
  1. 1.Department of Mathematic & Computer ScienceKent State UniversityKentUSA
  2. 2.Department of MathematicsTechnion - Israel Institute of TechnologyHaifaIsrael
  3. 3.School of Mathematical SciencesTel Aviv UniversityRamat Aviv, Tel AvivIsrael

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