Compact operator (source code)

= Compact operator
{wiki=Compact_operator}

In functional analysis, a compact operator is a specific type of linear operator that maps elements from one Banach space to another (or possibly to the same space) with properties similar to those of compact sets in finite-dimensional spaces. The concept of compact operators is crucial in the study of various problems in applied mathematics, quantum mechanics, and functional analysis. \#\#\# Definition Let \\( X \\) and \\( Y \\) be two Banach spaces.