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Nuclear space
... by some family of seminorms. For any seminorm, the unit ball is a closed convex ... 0 is the unit ball of some seminorm. (For complex vector spaces, the condition "symmetric ... replaced by "balanced".) If p is a seminorm on V, we write V p for ... topological vector space such that for any seminorm p we can find a larger seminorm q so that the natural map ...
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Talk:Norm (mathematics)
... July 2005 11:58 (UTC) turning a seminorm into a norm Somehow I seem to ... associated with the process of turning a seminorm into a norm by modding out by ... modulo the subspace of vectors of zero seminorm, on which the (induced) seminorm (the seminorm is independent of the representative of ...
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Talk:Locally convex topological vector space
... 33, 11 May 2004 (UTC) OK, created Seminorm -- Andrew Kepert 06:27, 11 May 2004 ... β (x,y)=q β (y). A seminorm is, after all just projection onto one ... And every LCTVS with countable family of seminorm is metrizable, not just semimetrizable. (Actually, I ... and read the articles on convex or seminorm to get these, I note that those ... appropriate to define convex, absorbent, balanced and seminorm here in the article, but I ...
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Locally convex topological vector space
... convex set as a subset. Seminorms A seminorm on V is a map p:V ... if follows that μ C is a seminorm if C is balanced and convex (it ... that for every ε > 0 and every seminorm p α , there exists a κ such ... the space is induced from a single seminorm, then the space seminormable. Any locally convex ... alpha_n}(x)). In other words, each seminorm of the range of T is ...
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Kolmogorov space
... is not really a norm, only a seminorm, because there are functions other than the ... a vector space, and it has a seminorm, and these define a pseudometric and a ... properties of these structures; for example, the seminorm satisfies the parallelogram identity and the uniform ... the space is now T 0 . A seminorm is a norm iff the underlying topology ... people came up with the definition of seminorm as well, which is a sort ...
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Normed vector space
... spaces (in particular, Banach spaces) involves a seminorm defined on a vector space and then ... space by the subspace of elements of seminorm zero. For instance, with the L p ... dx \right)^{1/p} is a seminorm on the vector space of all functions ... side is defined and finite. However, the seminorm is equal to zero for any function ... normed space and a space with trivial seminorm. Consequently, many of the more interesting ...
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Standard (maths) (translated from Dutch)
... math> for ) Seminorm A function which meets conditions 2 and ... to condition 1, one does not call seminorm. The method with which a normalised space ... metrische space becomes, makes of semigenormeerde space (seminorm) pseudometrische a space (pseudometriek). The vectors of which amount to the seminorm 0, form in that case vector space ...
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Talk:Discontinuous linear map
... is already in the definition of the seminorm, all it does is increment the index to the next seminorm in the family. So I conclude that ... functional is (rather, gives rise to) a seminorm. So we might mention the Fréchet LCTVSes ...
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Minkowski functionally (translated from German)
... like that is a Seminorm. Turned around for each Seminorm the quantity |
Semi-Hilbert space
... so that it gives rise to a seminorm rather than a vector space norm. The ... this space by the kernel of this seminorm is also required to be a Hilbert ...
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