weak* convergence in normed linear space

• $(x_n^{\prime })\subset X^{\prime }$

• $X$ a Banach space

• $\exists x^{\prime }\in X^{\prime }:\forall x\in X:{lim}_{n\to \mathrm{\infty }}x(x_n^{\prime })\equiv x_n^{\prime }(x)=x^{\prime }(x)$.

• If $X$ is reflexive (http://planetmath.org/DualSpace), then weak* convergence is the same as weak convergence

Note: This is a “seed” entry written using a short-hand format described in this FAQhttp://www.ma.utexas.edu/ jcorneli/h/FAQ/.

Title	weak* convergence in normed linear space
Canonical name	WeakConvergenceInNormedLinearSpace
Date of creation	2013-03-22 14:02:20
Last modified on	2013-03-22 14:02:20
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	9
Author	bwebste (988)
Entry type	Definition
Classification	msc 46B10
Related topic	WeakConvergence