Multilinear operators between asymmetric normed spaces
Volume 161 / 2020
Colloquium Mathematicum 161 (2020), 157-171
MSC: Primary 46E10; Secondary 47H60.
DOI: 10.4064/cm7814-6-2019
Published online: 11 March 2020
Abstract
We introduce and characterize the continuity of multilinear mappings between asymmetric normed spaces. In particular, we study the completeness properties of the asymmetric normed semilinear space of these mappings. As an application, we prove multilinear versions of the Banach–Steinhaus and closed graph theorems in the framework of asymmetric normed spaces.
