Assume you have an operator $T : \operatorname{dom(T)}\rightarrow H$. Now we also know that $ran(T)$ is finite-dimensional. Does this imply that $T$ is bounded?( So is $T$ a bounded map $T \in L(dom(T),H)$)?
2026-04-08 10:48:40.1775645320
Unbounded operator
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No. For example, unbounded linear functionals do exist.