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Let $V$ be a (Hausdorff) topological vector space, $W\subset V$ a closed linear subspace, $X\subset V $ a compact. (Q): When there is a continuous map $P:X\to W$ such that $P(x)=x$ for every $x\in X\...

It is well-known that the space of compact operators over Banach spaces is closed within the norm topology. My question: Let $X$ be a Banach space. Considering the strong topology (defined by ...