dual space

Noun

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Noun

**dual space** (*plural* dual spaces)

- (
*mathematics*) The vector space which comprises the set of linear functionals of a given vector space. - (
*mathematics*) The vector space which comprises the set of continuous linear functionals of a given topological vector space.**2011**, David E. Stewart,*Dynamics with Inequalities*, Society for Industrial and Applied Mathematics, page 17 ↗,- The
**dual space**of a Banach space X is the vector space of continuous linear functions X \rightarrow\mathbb{R}, which are called functionals. Similar notation is used for duality pairing between the Banach space X and its**dual space**X': \left\langle u, v\right\rangle is the result of applying the functional u \in X' to v \in X: \left\langle u, v\right\rangle = u(v) explicitly uses the fact that u is a function X \rightarrow\mathbb{R}.

- The

- (
*vector space of linear functionals*) algebraic dual space, dual vector space - (
*vector space of continuous linear functionals*) continuous dual space, continuous dual

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