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Complete Quasi-wandering Sets and Kernels of Functional Operators

  • Victor D. Didenko
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)

Abstract

Kernels of functional operators generated by mapping that possess complete quasi-wandering sets are studied. It is shown that the kernels of the operators under consideration either consist of a zero element or contain a subset isomorphic to a space \( L_\infty \left( \mathbb{S} \right) \)), where \( \mathbb{S} \subset \mathbb{R}^n \) has a positive Lebesgue measure. Consequently, such operators are Fredholm if and only if they are invertible.

Mathematics Subject Classification (2000)

Primary 47B33, 39A33, 45E10 Secondary 42C40, 39B42. 

Keywords

Quasi-wandering set homogeneous equation solution. 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Victor D. Didenko
    • 1
  1. 1.Department of MathematicsUniversity Brunei DarussalamBandar Seri BegawanBrunei

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