Compact operator on Hilbert space
= Compact operator on Hilbert space
{wiki=Compact_operator_on_Hilbert_space}
In functional analysis, a compact operator on a Hilbert space is a specific type of linear operator that has properties similar to matrices but extended to infinite dimensions. To give a more formal definition, consider the following: Let \\( H \\) be a Hilbert space. A bounded linear operator \\( T: H \\to H \\) is called a **compact operator** if it maps bounded sets to relatively compact sets.