Factorization of the identity through operators with large diagonal

Laustsen, Niels Jakob and Lechner, Richard and Mueller, Paul (2018) Factorization of the identity through operators with large diagonal. Journal of Functional Analysis, 275 (11). pp. 3169-3207. ISSN 0022-1236

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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].

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Journal Article
Journal or Publication Title:
Journal of Functional Analysis
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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
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06 Mar 2018 14:58
Last Modified:
16 Sep 2023 01:39