weak* convergence in normed linear space

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$({x}_{n}^{\prime})\subset {X}^{\prime}$

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$X$ a Banach space^{}

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

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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 shorthand format described in \htmladdnormallinkthis FAQhttp://www.ma.utexas.edu/ jcorneli/h/FAQ/.
Title  weak* convergence in normed linear space 

Canonical name  WeakConvergenceInNormedLinearSpace 
Date of creation  20130322 14:02:20 
Last modified on  20130322 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 