Factorizing multilinear operators on Banach spaces, $C^{*}$-algebras and $JB^{*}$-triples
Volume 192 / 2009
Studia Mathematica 192 (2009), 129-146
MSC: Primary 46G25, 47H60, 47B10, 46L05, 17C65, 46L70.
DOI: 10.4064/sm192-2-3
Abstract
In recent papers, the Right and the Strong$^*$ topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong$^{*}$-to-norm continuity of a multilinear operator $T$ defined on $C^{*}$-algebras (respectively, $JB^{*}$-triples) to $C^{*}$-summability (respectively, $JB^*$-triple-summability).
