The Kato decomposition of quasi-Fredholm relations

J.-Ph. Labrousse, A. Sandovici, H.S.V. de Snoo, H. Winkler

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    28 Citations (Scopus)

    Abstract

    Quasi-Fredholm relations of degree d is an element of N in Hilbert spaces are defined in terms of conditions on their ranges and kernels. They are completely characterized in terms of an algebraic decomposition with a quasi-Fredholm relation of degree 0 and a nilpotent operator of degree d. The adjoint of a quasi-Fredholm relation of degree d is an element of N is shown to be quasi-Fredholm relation of degree d is an element of N. The class of quasi-Fredholm relations contains the semi-Fredholm relations. Earlier results for quasi-Fredholm operators and semi-Fredholm operators are included.

    Original languageEnglish
    Pages (from-to)1-51
    Number of pages51
    JournalOperators and matrices
    Volume4
    Issue number1
    Publication statusPublished - Mar-2010

    Keywords

    • Quasi-Fredholm relation
    • semi-Fredholm relation
    • Kato decomposition
    • LINEAR RELATIONS
    • OPERATORS
    • SPACES

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