Let $V$ be a normed vector space (not necessarily a Banach space) and let $S$ and $T$ be continuous linear transformations from $V$ to $V$. If we assume that $T=T \circ S \circ T$. Then how to show that $T(V)$ is a closed subspace of $V$? Thank you for your help!
$T(V)$ is a closed subspace of $V$?
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functional-analysis
operator-theory
normed-spaces