, an asymmetric norm
on a vector space
is a generalization of the concept of a norm
Let X be a real vector space. Then an asymmetric norm on X is a function p : X → R satisfying the following properties:
- is an asymmetric norm but not a norm.
- More generally, given a strictly positive function g : Sn−1 → R defined on the unit sphere Sn−1 in Rn (with respect to the usual Euclidean norm |·|, say), the function p given by
- is an asymmetric norm on Rn but not necessarily a norm.
- Cobzaş, S. (2006). "Compact operators on spaces with asymmetric norm". Stud. Univ. Babeş-Bolyai Math. 51 (4): 69–87.