ScalingStacks

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.