Adjoint space
From Encyclopedia of Mathematics
of a topological vector space
The vector space consisting of continuous linear functions on
. If
is a locally convex space, then the functionals
separate the points of
(the Hahn–Banach theorem). If
is a normed space, then
is a Banach space with respect to the norm
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There are two (usually different) natural topologies on which are often used: the strong topology determined by this norm and the weak-
-topology.
References
[1] | D.A. Raikov, "Vector spaces" , Noordhoff (1965) (Translated from Russian) |
Comments
Instead of the term adjoint space one more often uses the term dual space. The weak--topology on
is the weakest topology on
for which all the evaluation mappings
,
,
, are continuous.
References
[a1] | H.H. Schaefer, "Topological vector spaces" , Macmillan (1966) |
How to Cite This Entry:
Adjoint space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_space&oldid=17289
Adjoint space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_space&oldid=17289