Strongly factorable multilinear operators on Banach spaces
Volume 154 / 2018
Colloquium Mathematicum 154 (2018), 15-30
MSC: Primary 47L22, 46G25, 46B28, 46A32; Secondary 47L20, 47B10.
DOI: 10.4064/cm7269-12-2017
Published online: 18 June 2018
Abstract
We prove that for every ideal $\cal M$ of multilinear operators on Banach spaces there exists an ideal ${\cal M}^{\rm fac}$ such that every $n$-linear operator $A$ in ${\cal M}^{\rm fac}$ is strongly $\cal M$-factorable in the sense that it factors through multilinear operators in $\cal M$ with respect to any partition of $\{1, \ldots ,n\}$. We compute ${\cal M}^{\rm fac}$ for some important ideals ${\cal M}$ and we show that the passage from $\cal M$ to ${\cal M}^{\rm fac}$ is advantageous in the sense that ${\cal M}^{\rm fac}$ enjoys some properties that ${\cal M}$ may not enjoy.
