Hilbert space factorization and Fourier type of operators
Tom 145 / 2001
Studia Mathematica 145 (2001), 199-212
MSC: 47L20, 47B10, 47D50.
DOI: 10.4064/sm145-3-2
Streszczenie
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.
