# weak* convergence in normed linear space

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

• $X$ a Banach space

• $\exists x^{\prime}\in X^{\prime}:\forall x\in X:\lim_{n\rightarrow\infty}x(x^{% \prime}_{n})\equiv x^{\prime}_{n}(x)=x^{\prime}(x)$.

• 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 \htmladdnormallinkthis FAQhttp://www.ma.utexas.edu/ jcorneli/h/FAQ/.

Title weak* convergence in normed linear space WeakConvergenceInNormedLinearSpace 2013-03-22 14:02:20 2013-03-22 14:02:20 bwebste (988) bwebste (988) 9 bwebste (988) Definition msc 46B10 WeakConvergence