in order theory and functional analysis, an abstract L-space, an AL-space, or an abstract Lebesgue space is a Banach lattice ( X , ‖ ⋅ ‖ ) {\displaystyle...

L-space may refer to: The classical function spaces Lp and ℓ p {\displaystyle \ell ^{p}} L-space (topology), a hereditarily Lindelöf space The Banach lattice...

The concept of an abstract Wiener space is a mathematical construction developed by Leonard Gross to understand the structure of Gaussian measures on...

usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that...

inequality). Abstractly speaking, this means that R n {\displaystyle \mathbb {R} ^{n}} together with the p {\displaystyle p} -norm is a normed vector space. Moreover...

generalize to abstract (L)-spaces. Banach space – Normed vector space that is complete Normed vector lattice Riesz space – Partially ordered vector space, ordered...

of what "basic functions", or, in abstract Hilbert spaces, what basic vectors suffice to generate a Hilbert space H , {\displaystyle H,} in the sense...

Abstract expressionism in the United States emerged as a distinct art movement in the aftermath of World War II and gained mainstream acceptance in the...

said to be a realization of an abstract polytope in some real N-dimensional space, typically Euclidean. This abstract definition allows more general combinatorial...

coined the term Hilbert space for the abstract concept that underlies many of these diverse applications. The success of Hilbert space methods ushered in a...

in the concrete set L {\displaystyle L} to an element α ( x ) {\displaystyle \alpha (x)} in the abstract set L ′ {\displaystyle L'} . That is, element...

is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces. As zero-dimensional...

of abstract (L)-spaces and the mean ergodic theorem." Annals of Mathematics (1941): 523–537. doi:10.2307/1968915 "Concrete representation of abstract (M)-spaces...

continuity and convergence. To put it more abstractly every seminormed vector space is a topological vector space and thus carries a topological structure...

2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick. The screenplay was written by Kubrick and Arthur C...

form the basis for other abstract data types including the queue, the stack, and their variations. The abstract list type L with elements of some type...

In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node...

linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological vector spaces (TVSs) X {\displaystyle X} and Y {\displaystyle...

admit the structure of a metric space, including Riemannian manifolds, normed vector spaces, and graphs. In abstract algebra, the p-adic numbers arise...

abstract operations of O {\displaystyle O} . For instance, there is a Lie operad L {\displaystyle L} such that the algebras over L {\displaystyle L}...

rigged Hilbert space places this idea in an abstract functional-analytic framework. Formally, a rigged Hilbert space consists of a Hilbert space H, together...

that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space. It was...

especially in an area of abstract algebra known as representation theory, a faithful representation ρ of a group G on a vector space V is a linear representation...

A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects...

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates)...

instance an abstract simplicial complex of infinite dimension. However, the following more abstract construction provides a topological space for any kind...

studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic...

such spaces are open to all, while private property is the land culturally owned by an individual or company, for their own use and pleasure. Abstract space...

subcomplex of Δ is an abstract simplicial complex L such that every face of L belongs to Δ; that is, L ⊆ Δ and L is an abstract simplicial complex. A...

extensively in abstract algebra and homological algebra, where tensors arise naturally. Given a finite set {V1, ..., Vn} of vector spaces over a common...