Let be asymmetric normed spaces and the convex cone of all linear continuous operators from to . It is known that in general, is not a vector space. The aim of this note is to give, using the Baire category theorem, a complete characterization on and a finite dimensional so that is a vector space. For this, we introduce an index of symmetry of the space denoted and we give the link between the index and the fact that is in turn an asymmetric normed space for every asymmetric normed space . Our study leads to a topological classification of asymmetric normed spaces.
"Index of symmetry and topological classification of asymmetric normed spaces." Rocky Mountain J. Math. 50 (6) 1951 - 1964, December 2020. https://doi.org/10.1216/rmj.2020.50.1951