English

On normed products of operator ideals which contain $\frak{L}_2$ as a factor

Functional Analysis 2007-05-23 v1

Abstract

We investigate quasi-Banach operator ideal products (AB,AB)({\frak{A}}\circ{\frak{B}},\mathbf{A\circ B}) which contain (L2,L2)(\frak{L}_2, \mathbf{L}_2) as a factor. In particular, we ask for conditions which guarantee that AB\mathbf{A\circ B} is even a norm if each factor of the product is a 1-Banach ideal. In doing so, we reveal the strong influence of the existence of such a norm in relation to the accessibility of the product ideal and the structure of its factors.

Keywords

Cite

@article{arxiv.math/0108123,
  title  = {On normed products of operator ideals which contain $\frak{L}_2$ as a factor},
  author = {Frank Oertel},
  journal= {arXiv preprint arXiv:math/0108123},
  year   = {2007}
}