Functional analysis
label: Analyse fonctionnelle (mathématiques) @fr
label: 関数解析学 @ja
label: تحليل دالي @ar
label: Anàlisi funcional @ca
label: Функціональний аналіз @uk
label: Funkcionální analýza @cs
label: Συναρτησιακή ανάλυση @el
label: Функциональный анализ @ru
label: Análise funcional @pt
label: Análisis funcional @es
label: Funktionalanalysis @de
label: Analisis fungsional @in
label: Analisi funzionale @it
label: Funktionalanalys @sv
label: Functionaalanalyse @nl
label: 함수해석학 @ko
label: Analiza funkcjonalna @pl
label: 泛函分析 @zh
name: Closed graph theorem
name: Spectral theorem
name: Hahn–Banach theorem:
name: Theorem
name: Open mapping theorem
description: matematiikan osa-alue @fi
description: gren af matematik @da
description: Zweig der Mathematik @de
description: studfako de analitiko pri nefinidimensiaj topologiaj vektoraj spacoj @eo
description: a matematikai analízisnek a funkcionálok és lineáris operátorok tulajdonságait vizsgáló ága @hu
description: 數學嘅一個分支，主要研究無限維拓撲向量空間，好多時都係函數空間 @yue
description: rama de las matemáticas @es
description: Дял от математиката @bg
description: branca de les matemàtiques @ca
description: раздел анализа, в котором изучаются бесконечномерные топологические векторные пространства и их отображения @ru
description: フーリエ変換や微分方程式、積分方程式などの研究に端を発している解析学 @ja
description: matematikaren adarra @eu
description: settore dell'analisi matematica @it
description: анализдың сикһеҙ үлсәмле топологик векторлы арауыҡтар һәм уларҙың сағылыштары өйрәнелгән бүлеге. @ba
description: grein av matematisk analyse @nn
description: matematická disciplína studující prostory nekonečné dimenze a zobrazení mezi nimi @cs
description: gren inom matematiken @sv
description: dział matematyki wyższej @pl
description: branch of mathematical analysis concerned with infinite-dimensional topological vector spaces, often spaces of functions
description: branche de l'analyse qui étudie les espaces de fonctions @fr
description: matematiche @co
subject: Category:Functional analysis
math statement: If is a sublinear function, and is a linear functional on a linear subspace which is dominated by on ; that is, then there exists a linear extension of to the whole space which is dominated by on ; that is, there exists a linear functional such that
math statement: Let be a Banach space and be a normed vector space. Suppose that is a collection of continuous linear operators from to . If for all in one has then
math statement: If is a topological space and is a compact Hausdorff space, then the graph of a linear map from to is closed if and only if is continuous.
math statement: Let be a bounded self-adjoint operator on a Hilbert space . Then there is a measure space and a real-valued essentially bounded measurable function on and a unitary operator such that where T is the multiplication operator: and .
math statement: If and are Banach spaces and is a surjective continuous linear operator, then is an open map .
b: Functional Analysis
commons: no
d: no
date: 2021-10-28
date: 2017-04-01
id: p/f042020
n: no
q: Functional analysis
s: no
species: no
title: Functional analysis
url: https://web.archive.org/web/20211028084954/http:/www.ebook3000.com/Theory-of-Linear-Operations--Volume-38--North-Holland-Mathematical-Library--by-S--Banach_134628.html
url: https://web.archive.org/web/20170401143239/http:/www.uccs.edu/~gmorrow/
v: no
voy: no
wikt: no
hypernym: Branch