functional analysis, a seminorm is a norm that need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm is the Minkowski...

quasi-seminorm or a Banach functional, on a vector space X {\displaystyle X} is a real-valued function with only some of the properties of a seminorm. Unlike...

with a seminorm is called a seminormed vector space. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". A...

multiple of an F-seminorm (resp. F-norm, seminorm) is again an F-seminorm (resp. F-norm, seminorm). The sum of finitely many F-seminorms (resp. F-norms)...

Grothendieck. The topology on nuclear spaces can be defined by a family of seminorms whose unit balls decrease rapidly in size. Vector spaces whose elements...

Alternatively they can be defined as a vector space with a family of seminorms, and a topology can be defined in terms of that family. Although in general...

|F|\leq p.} Every norm is a seminorm and both are symmetric balanced sublinear functions. A sublinear function is a seminorm if and only if it is a balanced...

quasi-seminorm) whose multiplier is 1. {\displaystyle 1.} Thus every seminorm is a quasi-seminorm and every norm is a quasinorm (and a quasi-seminorm). If...

with a norm. A seminormed vector space is a vector space equipped with a seminorm. A useful variation of the triangle inequality is ‖ x − y ‖ ≥ | ‖ x ‖ −...

that it gives rise to a seminorm rather than a vector space norm. The quotient of this space by the kernel of this seminorm is also required to be a...