Compact Operators

Compactness of an operator goes one step beyond continuity. Its treatment is fundamental in many areas in Applied Analysis, particularly Differential Equations and Variational Methods. Since compactness is one of the main concepts in Topology when applied to Analysis, compact operators will also play a fundamental role. In some sense, the class of compact operators is the one that allows to shift our intuition about finite-dimensional spaces to the infinite-dimensional scenario.