Perturbation of Operators and Applications to Frame Theory

Ole Christensen, P. Casazza

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    A celebrated classical result states that an operator U on a Banach space is invertible if it is close enough to the identity operator I in the sense that ||I - U|| < 1. Here Mle show that U actually is invertible under a much weaker condition. As an application we prove new theorems concerning stability of frames (and frame-like decompositions) under perturbation in both Hilbert spaces and Banach spaces.
    Original languageEnglish
    JournalJournal of Fourier Analysis and Applications
    Volume3
    Issue number5
    Pages (from-to)543-557
    ISSN1069-5869
    DOIs
    Publication statusPublished - 1997

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