Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11012931 | Journal of Functional Analysis | 2018 | 31 Pages |
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 1â¤p,q<â, with the bi-parameter Haar system, this problem always has a positive solution. The spaces Lp,1
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Niels Jakob Laustsen, Richard Lechner, Paul F.X. Müller,