Analyse fonctionnelle (mathématiques)
関数解析学
تحليل دالي
Anàlisi funcional
Функціональний аналіз
Funkcionální analýza
Functional analysis
Συναρτησιακή ανάλυση
Функциональный анализ
Análise funcional
Análisis funcional
Funktionalanalysis
Analisis fungsional
Analisi funzionale
Funktionalanalys
Functionaalanalyse
함수해석학
Analiza funkcjonalna
泛函分析
Closed graph theorem
Spectral theorem
Hahn–Banach theorem:
Theorem
Open mapping theorem
matematiikan osa-alue
gren af matematik
Zweig der Mathematik
studfako de analitiko pri nefinidimensiaj topologiaj vektoraj spacoj
a matematikai analízisnek a funkcionálok és lineáris operátorok tulajdonságait vizsgáló ága
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
rama de las matemáticas
Дял от математиката
branca de les matemàtiques
раздел анализа, в котором изучаются бесконечномерные топологические векторные пространства и их отображения
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
matematikaren adarra
settore dell'analisi matematica
анализдың сикһеҙ үлсәмле топологик векторлы арауыҡтар һәм уларҙың сағылыштары өйрәнелгән бүлеге.
grein av matematisk analyse
matematická disciplína studující prostory nekonečné dimenze a zobrazení mezi nimi
gren inom matematiken
dział matematyki wyższej
branch of mathematical analysis concerned with infinite-dimensional topological vector spaces, often spaces of functions
branche de l'analyse qui étudie les espaces de fonctions
matematiche
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
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
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.
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 .
If and are Banach spaces and is a surjective continuous linear operator, then is an open map .
Functional Analysis