- 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...
- 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...
- {\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 ′ ′ ,...
- 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...
- 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...
- 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...
-
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...
-
continuous dual space.
Alexander Grothendieck characterized the
strong dual and
bidual for
certain situations: Theorem (Grothendieck) — Let N {\displaystyle N}...
-
embedding J {\displaystyle J} of L p ( μ ) {\displaystyle L^{p}(\mu )} into its
bidual. Moreover, the map j p {\displaystyle j_{p}} is onto, as
composition of...
-
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...
