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Compact operator

In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional operator such as a matrix. In infinite-dimensional spaces, bounded sets are usually not compact, and bounded sequences need not have convergent subsequences. Compact operators partly restore this…

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Overview

Definitions

Basic properties

Fredholm theory

Spectral theory

Compact operators on Hilbert spaces

Completely continuous operators

Examples and non-examples

Compact embeddings

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Map overview Semantic statistics

Compact operator

Nodes78
Edges77
Triples68
Avg. degree1.97
Density0.025641
Components1

How this topic connects Entity context

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Compact operator

Top relations

related to Approximation by finite-rank operators · 10
Compact operator → Alexander Grothendieck, Banach, For, Hilbert, On Hilbert, Per Enflo, Since, Stefan Banach, The, Whether
related to Compact operators on Hilbert spaces · 6
Compact operator → Banach-space, Compact, Hermitian, Hilbert, Hilbert-space, In
related to Examples and non-examples · 6
Compact operator → Finite-rank, For, If, In, One, Thus
related to Fredholm theory · 6
Compact operator → Banach, Compact, Fredholm, Let, Then, This
related to Motivation: integral equations · 6
Compact operator → Arzelà, Ascoli, By, Compact, Thus, Under
related to Spectral theory · 6
Compact operator → Apart, Banach, Let, More, The, Then
related to Singular-value expansion · 5
Compact operator → Hilbert, If, Nevertheless, There, They
related to Algebraic properties · 4
Compact operator → Banach, Compact, Equivalently, If
related to Completely continuous operators · 4
Compact operator → Banach, Compact, However, Let
related to Basic properties · 3
Compact operator → Banach, The, Throughout

Important terminology Word statistics

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Important terminology

compact displaystyle operator bounded spaces operators finite-dimensional space banach every linear sequence spectrum isbn compactness nonzero hilbert integral functions many

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Compact operatoris alinear operator that behaves0.90text
a matrixinstance oflike a finite-dimensional operator0.80text
those in the Rellichinstance ofThus compactness of embeddings0.80text
Compact operatorrelated to Algebraic propertiesIf0.60section
Compact operatorrelated to Algebraic propertiesBanach0.60section
Compact operatorrelated to Algebraic propertiesEquivalently0.60section
Compact operatorrelated to Algebraic propertiesCompact0.60section
Compact operatorrelated to Approximation by finite-rank operatorsSince0.60section
Compact operatorrelated to Approximation by finite-rank operatorsOn Hilbert0.60section
Compact operatorrelated to Approximation by finite-rank operatorsHilbert0.60section
Compact operatorrelated to Approximation by finite-rank operatorsFor0.60section
Compact operatorrelated to Approximation by finite-rank operatorsBanach0.60section

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