Dictionary

dual space en · NOUN

Meanings

1. The vector space which comprises the set of linear functionals of a given vector space.
2. 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:

Forms

Synonyms

dual vector space (vector space of linear functionals) · continuous dual (vector space of continuous linear functionals) · algebraic dual space (vector space of linear functionals) · continuous dual space (vector space of continuous linear functionals)