 Hellinger–Toeplitz theorem

The Hellinger–Toeplitz theorem is a result in functional analysis that characterizes certain types of operators, specifically compact operators on Hilbert spaces. It states that if \( T \) is a compact linear operator on a Hilbert space \( H \), then the following conditions are equivalent: 1. \( T \) is a compact operator. 2. The image under \( T \) of the unit ball in \( H \) is relatively compact in \( H \) (i.