Weighted Shifts on Directed Trees

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A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weigh…

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    Om Weighted Shifts on Directed Trees

    A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality, cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights. Related questions that arose during the study of the topic are solved as well.

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    Detaljer

    Format
    E-Bok
    Kopisperre
    Teknisk DRM
    Filformat
    PDF
    Forlag
    American Mathematical Society
    Språk
    Engelsk
    ISBN
    9780821885277
    Sider
    107

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