Do we have any result that could say something like: "If you have an operator $T\in\mathcal{L}(X)$ with certain rank (possibly infinite) and if you take $\epsilon>0$ small then all the operators in $B(T;\epsilon)$ has rank at least something" ?
2026-03-16 19:44:14.1773690254
Minimum rank of the operators in a neighborhood
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