weak* convergence in normed linear space

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$(x^{\\prime}_{n})\\subset X^{\\prime}$
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$X$ a Banach space
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$\\exists x^{\\prime}\\in X^{\\prime}:\\forall x\\in X:\\lim_{n\\rightarrow\\infty}x(x^{%\\prime}_{n})\\equiv x^{\\prime}_{n}(x)=x^{\\prime}(x)$ .
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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 short-hand format described in \\htmladdnormallinkthis FAQhttp://www.ma.utexas.edu/ jcorneli/h/FAQ/.

单词	WeakConvergenceInNormedLinearSpace
释义	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/.
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