All Functional and Operator Analysis

Branches that treat functions as points of infinite dimensional spaces and study the operators acting between those spaces. An entry belongs here when its cited source describes Banach and Hilbert spaces, bounded and unbounded linear operators, spectral theory, or operator algebras. It does not belong here when the branch is mainly about decomposing a function into frequencies or approximating it by simpler functions, which are in the harmonic analysis and approximation group. The group is the abstract setting in which much of modern analysis and quantum theory is written.