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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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Given projection PP is weak-star to weak-star continuous [closed]
Let $X$ be a Banach space, and $P$ be a projection of $X^*$ such that $\Vert P \Vert\leq 1$ and $\ker(P)$, ${\bf ran}(1-p)$ are weak-star closed. Show that $P$
is weak-star to weak-star continuous.
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