Source: wikibot/hilbert-schmidt-theorem
= Hilbert–Schmidt theorem
{wiki=Hilbert–Schmidt_theorem}
The Hilbert–Schmidt theorem is a result in functional analysis concerning the compact operators on a Hilbert space. Specifically, it provides a characterization of compact operators in terms of their approximation by finite-rank operators. In more detail, the theorem states the following: 1. **Hilbert Space**: Let \\( \\mathcal\{H\} \\) be a separable Hilbert space.