Corollary 2.6 . [00HA]

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Corollary 2.6.

Let $(V,\lVert\mathord{\cdot}\rVert_{V})$ and $(W,\lVert\mathord{\cdot}\rVert_{W})$ be Banach spaces over $k$ , and $f:V\rightarrow W$ be a bounded $k$ -linear map with closed image. Then $f$ is admissible.