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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

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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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