Let $\mathcal{B}(F)$ be the algebra of all bounded linear operators on a complex Hilbert space $F$.
Is $T\in \mathcal{B}(F)$ and bijective, is $T$ invertible? i.e. is $T^{-1}\in \mathcal{B}(F)$?
2026-04-01 02:00:11.1775008811
invertibility of a bounded linear operator
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If $T$ is bijective, then $T^{-1}\in \mathcal{B}(F)$. This is a consequence of the open mapping theorem.