normed functional
11Continuous linear extension — In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space X by first defining a linear transformation on a dense subset of X and then extending to the whole space via the theorem below.… …
12Topological vector space — In mathematics, a topological vector space is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a… …
13Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …
14Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …
15Bounded operator — In functional analysis, a branch of mathematics, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded by the same number, over all non zero… …
16Hahn–Banach theorem — In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear operators defined on a subspace of some vector space to the whole space, and it also shows that there are enough… …
17Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …
18Banach–Alaoglu theorem — In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu s theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. [Rudin, section …
19Projection (linear algebra) — Orthogonal projection redirects here. For the technical drawing concept, see orthographic projection. For a concrete discussion of orthogonal projections in finite dimensional linear spaces, see vector projection. The transformation P is the… …
20Banach space — In mathematics, Banach spaces (pronounced [ˈbanax]) is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every… …
