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Complemented subspace

In the branch of mathematics called functional analysis, a complemented subspace of a topological vector space X , {\displaystyle X,} is a vector subspace M {\displaystyle M} for which there exists some other vector subspace N {\displaystyle N} of X , {\displaystyle X,} called its (topological) complement in X {\displaystyle X} , such that X…

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Overview

Algebraic direct sum

Motivation

Definition

Examples

Sufficient conditions

Properties; examples of uncomplemented subspaces

Applications

In classical Banach spaces

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Complemented subspace

Nodes73
Edges72
Triples23
Avg. degree1.97
Density0.027397
Components1

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Complemented subspace

Top relations

related to Hilbert spaces · 7
Complemented subspace → Banach, Hilbert, Hilbert Banach, In, Joram Lindenstrauss, Lior Tzafriri, This
related to In classical Banach spaces · 7
Complemented subspace → Banach, For, Most, Such, The, These, Understanding
related to Properties; examples of uncomplemented subspaces · 5
Complemented subspace → Banach, From, Hamel, Hausdorff, Since
related to Indecomposable Banach spaces · 4
Complemented subspace → An, Banach, Because, The

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Important terminology

displaystyle spaces vector topological complemented continuous subspace space banach subspaces complement linear direct sum map algebraic oplus closed isbn oclc

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Complemented subspacerelated to Hilbert spacesIn0.60section
Complemented subspacerelated to Hilbert spacesHilbert0.60section
Complemented subspacerelated to Hilbert spacesThis0.60section
Complemented subspacerelated to Hilbert spacesBanach0.60section
Complemented subspacerelated to Hilbert spacesHilbert Banach0.60section
Complemented subspacerelated to Hilbert spacesJoram Lindenstrauss0.60section
Complemented subspacerelated to Hilbert spacesLior Tzafriri0.60section
Complemented subspacerelated to In classical Banach spacesUnderstanding0.60section
Complemented subspacerelated to In classical Banach spacesBanach0.60section
Complemented subspacerelated to In classical Banach spacesThe0.60section
Complemented subspacerelated to In classical Banach spacesFor0.60section
Complemented subspacerelated to In classical Banach spacesMost0.60section

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