Abstract
Let X,Y be asymmetric normed spaces and Lc(X,Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X,Y) is not a vector space. The aim of this note is to give, using the Baire category theorem, a complete characterization on X and a finite dimensional Y so that Lc(X,Y) is a vector space. For this, we introduce an index of symmetry of the space X denoted c(X)∈[0,1] and we give the link between the index c(X) and the fact that Lc(X,Y) is in turn an asymmetric normed space for every asymmetric normed space Y. Our study leads to a topological classification of asymmetric normed spaces.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
