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- branca de les matemàtiques (ca)
- gren af matematik (da)
- matematiikan osa-alue (fi)
- matematikaren adarra (eu)
- rama de las matemáticas (es)
- 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)
- matematická disciplína studující prostory nekonečné dimenze a zobrazení mezi nimi (cs)
- Zweig der Mathematik (de)
- branch of mathematical analysis concerned with infinite-dimensional topological vector spaces, often spaces of functions (en)
- dział matematyki wyższej (pl)
- grein av matematisk analyse (nn)
- gren inom matematiken (sv)
- a matematikai analízisnek a funkcionálok és lineáris operátorok tulajdonságait vizsgáló ága (hu)
- matematiche (co)
- settore dell'analisi matematica (it)
- раздел анализа, в котором изучаются бесконечномерные топологические векторные пространства и их отображения (ru)
- анализдың сикһеҙ үлсәмле топологик векторлы арауыҡтар һәм уларҙың сағылыштары өйрәнелгән бүлеге. (ba)
- 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)
- Дял от математиката (bg)
- studfako de analitiko pri nefinidimensiaj topologiaj vektoraj spacoj (eo)
- branche de l'analyse qui étudie les espaces de fonctions (fr)
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- 2017-04-01 (xsd:date)
- 2021-10-28 (xsd:date)
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- 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 . (en)
- 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 (en)
- If and are Banach spaces and is a surjective continuous linear operator, then is an open map . (en)
- 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 (en)
- 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. (en)
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- Theorem (en)
- Closed graph theorem (en)
- Hahn–Banach theorem: (en)
- Open mapping theorem (en)
- Spectral theorem (en)
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| rdfs:label
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- Functional analysis (en)
- Funktionalanalysis (de)
- تحليل دالي (ar)
- Anàlisi funcional (ca)
- Funkcionální analýza (cs)
- Συναρτησιακή ανάλυση (el)
- Analyse fonctionnelle (mathématiques) (fr)
- Análisis funcional (es)
- Analisis fungsional (in)
- Analisi funzionale (it)
- 関数解析学 (ja)
- 함수해석학 (ko)
- Functionaalanalyse (nl)
- Analiza funkcjonalna (pl)
- Análise funcional (pt)
- Функциональный анализ (ru)
- Функціональний аналіз (uk)
- Funktionalanalys (sv)
- 泛函分析 (zh)
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