Definition of Bidual. Meaning of Bidual. Synonyms of Bidual

- dual of B is A. In other cases the dual of the dual – the double dual or bidual – is not necessarily identical to the original (also called primal). Such...
- weakly*-dense in the unit ball of the bidual. In other words, for every x ″ {\displaystyle x''} in the bidual, there exists a net ( x i ) i ∈ I {\displaystyle...
- {\displaystyle X^{\prime }} is identical to the strong dual topology. The bidual or second dual of a TVS X , {\displaystyle X,} often denoted by X ′ ′ ,...
- for which the canonical evaluation map from X {\displaystyle X} into its bidual (which is the strong dual of the strong dual of X {\displaystyle X} ) is...
- its bidual, which is the dual of its dual space. The corresponding map is an isometry but in general not onto. A general Banach space and its bidual need...
- continuous dual space. Alexander Grothendieck characterized the strong dual and bidual for certain situations: Theorem (Grothendieck) — Let N {\displaystyle N}...
- onto a band in the order bidual. An order complete, regularly ordered vector lattice whose canonical image in its order bidual is order complete is called...
- injective natural map V → V∗∗, any vector space can be embedded into its bidual; the map is an isomorphism if and only if the space is finite-dimensional...
- that any locally compact abelian group is naturally isomorphic with its bidual (the dual of its dual). The Fourier inversion theorem is a special case...
- double dual or bidual of V. This canonical map is an isomorphism if V is finite-dimensional, and this allows identifying V with its bidual. (In the infinite-dimensional...