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

Abstract

We investigate quasi-Banach operator ideal products $(\mathfrak{A}\circ \mathfrak{B},\mathbf{A}\circ \mathbf{B})$ which contain $({\mathfrak{L}}_2,{\mathbf{L}}_2)$ as a factor. In particular, we ask for conditions which guarantee that $\mathbf{A}\circ \mathbf{B}$ 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.