dual space

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English[edit]

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Noun[edit]

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 is the vector space of continuous linear functions , which are called functionals. Similar notation is used for duality pairing between the Banach space and its dual space : is the result of applying the functional to : explicitly uses the fact that is a function .

Usage notes[edit]

Defined for all vector spaces, the dual space may, for clarity, be called the algebraic dual space. When defined for a topological vector space, the (algebraic) dual space has a subspace that corresponds to continuous linear functionals and is called the continuous dual space or continuous dual — or simply the dual space.

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