Double dual

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#REDIRECT Dual space#Injection into the double-dual

In mathematics, any vector space V has a corresponding double dual vector space (or just double dual for short) defined as the dual space of the dual space of V.

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In mathematics, the double dual is the dual of the dual of an object, for various definitions of duality. Examples include:

Algebraic vector space, $V^{**}$ : Dual space § Injection into the double-dual
Topological vector space, ⁠ $V''$ ⁠: Dual space § Double dual
Normed vector space, $V^{**}$ : Dual norm § The double dual of a normed linear space
Locally compact abelian group, ${\widehat {\widehat {G}}}$ : Pontryagin duality
Module, $M^{**}$ : Dual module