English
dual space
Noun

dual space (plural dual spaces)

1. (mathematics) The vector space which comprises the set of linear functionals of a given vector space.
2. (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}.
Synonyms
• (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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