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Oct 12, 2015 at 22:29 comment added Bill Johnson A space having that property is called a Grothendieck space. Reflexive spaces and injective spaces and combinations thereof are the standard examples. I don't think that there is any characterization of this class of spaces.
Oct 11, 2015 at 21:16 comment added Dongyang Chen This question may be stupid. It is well-known that on $l_{\infty}^{*}$, $weak^{*}$ convergent sequences are weakly convergent. Are there other spaces having this nice property besides $l_{\infty}$? Or what's the name of this property?
Oct 11, 2015 at 21:06 comment added Bill Johnson I have not seen such a characterization and cannot imagine what could be one.
Oct 11, 2015 at 0:58 history asked Dongyang Chen CC BY-SA 3.0