Bounded Linear Transformations on Hypernormed Vector Spaces

Madeleine Al Tahan, Bijan Davvaz

Abstract

The aim of this paper is to generalize normed vector spaces to hypernormed vector spaces. In this regards, we define hypernorm on hypervector space and investigate it's properties. Moreover, we introduce the notion of hypermetric space and use it to find a necessary and sufficient condition for two hypernorms on a hypervector space to be equivalent. Finally, we use hypernormed vector spaces to define bounded linear transformations and present some results related to them.