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 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.
