 Compact operator

A bounded operator is compact when it maps the unit ball to a relatively compact set.

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.