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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)

Abstract

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.

Keywords

Linear Subspace Complex Banach Space Linear Continuous Functional Spectral Subspace Invariant Closed Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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