## Is it true that if X is a separable banach space and M a inear manifold in the dual

that weak sequential closure M = weak star closure then M is sequentially dense?

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If you define your terms and provide some motivation you are more likely to get an answer. – Bill Johnson Apr 15 2012 at 20:03
Op here. M is just a linear subspace of X^*. Spaces where weak sequential closure is the same as ordinary closure (e.g. first countable spaces) are called Uryshon Fretchet spaces. Ive seen various characterizations of when M is sequentially dense in the dual of a separable space but none of them are very helpful. I'm trying to determine under what conditiosn M is a Uryshon Fretchet space. – Kale Apr 15 2012 at 20:40