Ideal extensions of classes of linear operators
Volume 247 / 2019
Studia Mathematica 247 (2019), 285-297
MSC: Primary 47L20; Secondary 47B10, 47B07.
DOI: 10.4064/sm171030-15-3
Published online: 27 December 2018
Abstract
We study the problem of extending classes of linear operators between Banach spaces to operator ideals. We establish necessary and sufficient conditions on a class $\mathfrak {B}$ of Banach spaces and on a class $ \cal O$ of operators taking values in Banach spaces belonging to $\mathfrak {B}$ guaranteeing that $ \cal O$ can be extended to an operator ideal. As applications we characterize the extendability of the class of quasi-$\tau (p)$-summing operators, we construct the operator ideal generated by an ideal of bilinear functionals and we prove that the class of weak$^*$-sequentially compact operators taking values in dual spaces is not extendable to an operator ideal.
