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Factorization of the identity through operators with large diagonal

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>2/03/2018
<mark>Journal</mark>Journal of Functional Analysis
<mark>State</mark>E-pub ahead of print
Early online date2/03/18
<mark>Original language</mark>English


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, ??, ?, 2018 DOI: 10.1016/j.jfa.2018.02.010