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
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Factorization of the identity through operators with large diagonal
AU - Laustsen, Niels Jakob
AU - Lechner, Richard
AU - Mueller, Paul
N1 - 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
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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, 1Studia Math. 1979].
AB - 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, 1Studia Math. 1979].
KW - Factorization of operators
KW - mixed-norm Hardy space
KW - Fredholm theory
KW - Gowers-Maurey space
U2 - 10.1016/j.jfa.2018.02.010
DO - 10.1016/j.jfa.2018.02.010
M3 - Journal article
VL - 275
SP - 3169
EP - 3207
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 11
ER -