The quotient of a Hilbert space by an equivalence relation which considers a pair of vectors equivalent iff they differ only by a factor which is a complex number.

In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis.

In functional analysis, a reproducing kernel Hilbert space is a Hilbert space of functions in which point evaluation is a continuous linear functional.

In the mathematical discipline of functional analysis, the concept of a compact operator on Hilbert space is an extension of the concept of a matrix acting on a finite-dimensional vector space; in Hilbert space, compact operators are precisely the closure of finite-rank operators (representable by finite-dimensional matrices) in the topology induced by the operator norm.