Multiplication and Compact-friendly Operators View Full Text


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Article Info

DATE

1997-06

AUTHORS

Y. A. Abramovich, C. D. Aliprantis, O. Burkinshaw

ABSTRACT

During the last few years the authors have studied extensively the invariant subspace problem of positive operators; see [6] for a survey of this investigation. In [4] the authors introduced the class of compact-friendly operators and proved for them a general theorem on the existence of invariant subspaces. It was then asked if every positive operator is compact-friendly. In this note, we present an example of a positive operator which is not compact-friendly but which, nevertheless, has a non-trivial closed invariant subspace. In the process of presenting this example, we also characterize the multiplication operators that commute with non-zero finite-rank operators. We show, among other things, that a multiplication operator Mϕ commutes with a non-zero finite-rank operator if and only the multiplier function ϕ is constant on some non-empty open set. More... »

PAGES

171-180

References to SciGraph publications

  • 1992-05. Positive operators on Krein spaces in ACTA APPLICANDAE MATHEMATICAE
  • 1986-03. Irreducible compact operators in MATHEMATISCHE ZEITSCHRIFT
  • Journal

    TITLE

    Positivity

    ISSUE

    2

    VOLUME

    1

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1009781922898

    DOI

    http://dx.doi.org/10.1023/a:1009781922898

    DIMENSIONS

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