Let $(H, \inp_H)$ and $(E, \inp_E)$ be [[Hilbert Space|Hilbert spaces]] with $H \subset E \subset H^*$, such that $H \subset E$ is [[Dense|densely]] and [[Compact Operator|compactly]] embedded, and $E \subset H^*$ is continuously embedded. Let $L: H \to H^*$ be a [[Bounded Linear Operator|bounded linear operator]], then by the [[Riesz Representation Theorem]], 1. $H \subset E \subset H^*$ with with the embeddings $H \subset E \subset H^*$ being compact, such that $H \subset E$