In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A : H → H {\displaystyle A\colon H\to H} that acts on a Hilbert space H {\displaystyle H} and has finite Hilbert–Schmidt norm where { e i : i ∈ I } {\displaystyle \{e_{i}:i\in I\}} is an orthonormal basis. Wikipedia