# dual space

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## dual space

[′dü·əl ′spās]
(mathematics)
The vector space consisting of all linear transformations from a given vector space into its scalar field.
References in periodicals archive ?
It puts its expertise and its means at the disposal of the defense which uses them in the framework of the preparation of the future and the conduct of military and dual space programs, but also of the surveillance of the space and the operations of satellites.
The book's decision to operate in the dual space of present and past allows it to feel fresh and at the same time detailed.
At weak coupling and for the chiral case, the effect of T-dualities was to pass to the dual space [p.sub.i] [right arrow] [x.sub.i] - [x.sub.i+1],[q.sub.i] [right arrow] [[theta].sub.i] - [[theta].sub.i+1] and one may hope to introduce a dual space for the nonchiral superspace in a similar way.
In the meantime, Smith discussed tempered distributions by focusing on distributional convolution and some of its application to signal analysis in [16] and showed the relationship between periodic tempered distributions, [S'.sub.1] and dual space of the smooth periodic functions, [P.sup.*.sub.p],in [17].
Heinrich and Mankiewicz [9] proved the infinite [[omega].sup.*]-Rademacher theorem: every Lipschitz mapping from a separable Banach space to the dual space of a separable Banach space is almost everywhere [[omega].sup.*]-Gateaux differentiable.
Since doors opened in September 2016, the dual space has offered residents of the town a vibrant community hub.
Suppose now X is a locally convex topological vector space and X* its dual space. Let X be equipped with the original topology T as well as the weak topology [T.sub.w], and WCC (X) ={A [subset.bar] X : A is a [T.sub.w]-compact convex subset of X} is the corresponding hyperspace.
Let us provide the dual space X' with the [weak.sup.*]- topology.
In this paper, we suppose that E is a reflexive Banach space with dual space [E.sup.*], and <*, *> denotes the pairing between E and [E.sup.*].
It is the same for bras, represented by line vectors, understood as covectors, that is, dual space elements.
The new facilities, which have been designed by Snook Architects, provide dual space meeting and seminar rooms, a library, canteen for staff and an IT infrastructure giving JB Leitch a base to liaise with its extensive client list.
Playing with relationships between two- and three-dimensionality, fullness and emptiness, outside and inside, this pen aluminum structure marks out a dual space measured in relationship to its surroundings, allowing one to see the virtual passage of time through its form.
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