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...
32 KB (6,140 words) - 12:55, 26 August 2024
Sublinear function (section Associated seminorm)
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...
22 KB (4,217 words) - 01:50, 28 August 2024
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...
34 KB (5,697 words) - 21:38, 16 August 2024
Metrizable topological vector space (redirect from F-seminorm)
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)...
64 KB (10,671 words) - 22:12, 18 January 2023
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...
27 KB (4,344 words) - 16:00, 8 May 2024
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...
58 KB (10,592 words) - 23:16, 10 August 2024
Hahn–Banach theorem (section For seminorms)
|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...
77 KB (12,643 words) - 19:21, 19 April 2024
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...
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Quasinorm (redirect from Quasi-seminorm)
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...
7 KB (960 words) - 18:18, 19 September 2023
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 ‖ −...
18 KB (2,890 words) - 22:11, 21 February 2024