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  • LLechnerMuellerJFAacceptedFeb2018

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 275, 11, 2018 DOI: 10.1016/j.jfa.2018.02.010

    Accepted author manuscript, 881 KB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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Factorization of the identity through operators with large diagonal

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<mark>Journal publication date</mark>1/12/2018
<mark>Journal</mark>Journal of Functional Analysis
Issue number11
Volume275
Number of pages39
Pages (from-to)3169-3207
Publication StatusPublished
Early online date2/03/18
<mark>Original language</mark>English

Abstract

Given a Banach space X with an unconditional basis, we consider the following question: does the identity operator on X factor through every operator on X with large diagonal relative to the unconditional basis? We show that on Gowers' unconditional Banach space, there exists an operator for which the answer to the question is negative. By contrast, for any operator on the mixed-norm Hardy spaces Hp(Hq), where 1≤p,q<∞, with the bi-parameter Haar system, this problem always has a positive solution. The spaces Lp, 1<p<∞, were treated first by Andrew [Studia Math. 1979].

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 275, 11, 2018 DOI: 10.1016/j.jfa.2018.02.010