Source: wikibot/kuiper-s-theorem
= Kuiper's theorem
{wiki=Kuiper's_theorem}
Kuiper's theorem is a result in the field of functional analysis, specifically within the study of Banach spaces and the theory of linear operators. It characterizes when a linear operator between two Banach spaces is compact. The theorem states that if \\( X \\) and \\( Y \\) are two Banach spaces, and if \\( T: X \\to Y \\) is a continuous linear operator, then the following are equivalent: 1. The operator \\( T \\) is compact.