dual space
noun1
Mathematics, Sciences The vector space which comprises the set of linear functionals of a given vector space.
2
Mathematics, Sciences The vector space which comprises the set of continuous linear functionals of a given topological vector space.
- The dual space of a Banach space X is the vector space of continuous linear functions X#92;rightarrow#92;mathbb#123;R#125;, which are called functionals. Similar notation is used for duality pairing between the Banach space X and its dual space X': #92;left#92;langleu,v#92;right#92;rangle is the result of applying the functional u#92;inX' to v#92;inX: #92;left#92;langleu,v#92;right#92;rangle#61;u(v) explicitly uses the fact that u is a function X#92;rightarrow#92;mathbb#123;R#125;.2011, David E. Stewart, Dynamics with Inequalities, Society for Industrial and Applied Mathematics, page 17:
- Synonyms
- algebraic dual space, dual vector space, continuous dual space, continuous dual