It is an open question whether every Fourier type 2 operator factors through a Hilbert space. We show that at least the natural gradations of Fourier type 2 norms and Hilbert space factorization norms are not uniformly equivalent. A corresponding result is also obtained for a number of other sequences of ideal norms instead of the Fourier type 2 gradation including the Walsh function analogue of Fourier type. Our main tools are ideal norms and random matrices.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-2,
author = {Aicke Hinrichs},
title = {Hilbert space factorization and Fourier type of operators},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {199-212},
zbl = {1059.47066},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-2}
}
Aicke Hinrichs. Hilbert space factorization and Fourier type of operators. Studia Mathematica, Tome 147 (2001) pp. 199-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-2/