Adjoint space

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

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)