@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-LLND57KL-D
  skos:prefLabel "algèbre associative"@fr, "associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-WLMG00CZ-5 .

psr:-V40NLNFZ-K
  skos:prefLabel "C*-algebra"@en, "C*-algèbre"@fr ;
  a skos:Concept ;
  skos:broader psr:-WLMG00CZ-5 .

psr:-WLMG00CZ-5
  a skos:Concept ;
  skos:definition """En mathématiques, l'algèbre de Banach est une des structures fondamentales de l'analyse fonctionnelle, portant le nom du mathématicien polonais Stefan Banach (1892-1945). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Banach">https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Banach</a>)"""@fr, """In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle A}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>A</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle A}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="A"></span> over the <a href="/wiki/Real_number" title="Real number">real</a> or <a href="/wiki/Complex_number" title="Complex number">complex</a> numbers (or over a <a href="/wiki/Nonarchimedean_field" class="mw-redirect" title="Nonarchimedean field">non-Archimedean</a> complete <a href="/wiki/Norm_(mathematics)" title="Norm (mathematics)">normed field</a>) that at the same time is also a <a href="/wiki/Banach_space" title="Banach space">Banach space</a>, that is, a <a href="/wiki/Normed_space" class="mw-redirect" title="Normed space">normed space</a> that is <a href="/wiki/Complete_metric_space" title="Complete metric space">complete</a> in the <a href="/wiki/Metric_(mathematics)" class="mw-redirect" title="Metric (mathematics)">metric</a> induced by the norm. The norm is required to satisfy
         over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy
         <br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\|x\\\\,y\\\\|\\\\ \\\\leq \\\\|x\\\\|\\\\,\\\\|y\\\\|\\\\quad {\\	ext{ for all }}x,y\\\\in A.}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
         <mi>x</mi>
         <mspace width="thinmathspace"></mspace>
         <mi>y</mi>
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
         <mtext> </mtext>
         <mo>≤<!-- ≤ --></mo>
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
         <mi>x</mi>
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
         <mspace width="thinmathspace"></mspace>
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
         <mi>y</mi>
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
         <mspace width="1em"></mspace>
         <mrow class="MJX-TeXAtom-ORD">
         <mtext> for all </mtext>
         </mrow>
         <mi>x</mi>
         <mo>,</mo>
         <mi>y</mi>
         <mo>∈<!-- ∈ --></mo>
         <mi>A</mi>
         <mo>.</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\|x\\\\,y\\\\|\\\\ \\\\leq \\\\|x\\\\|\\\\,\\\\|y\\\\|\\\\quad {\\	ext{ for all }}x,y\\\\in A.}</annotation>
         </semantics>
         </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ee50193268a5594d400efba5524689d19a94dd6" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.455ex; height:2.843ex;" alt="{\\\\displaystyle \\\\|x\\\\,y\\\\|\\\\ \\\\leq \\\\|x\\\\|\\\\,\\\\|y\\\\|\\\\quad {\\	ext{ for all }}x,y\\\\in A.}"></div>
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Banach_algebra">https://en.wikipedia.org/wiki/Banach_algebra</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Alg%C3%A8bre_de_Banach>, <https://en.wikipedia.org/wiki/Banach_algebra> ;
  skos:broader psr:-LLND57KL-D, psr:-HX2VX066-P ;
  skos:narrower psr:-V40NLNFZ-K ;
  skos:inScheme psr: ;
  skos:prefLabel "Banach algebra"@en, "algèbre de Banach"@fr .

psr:-HX2VX066-P
  skos:prefLabel "functional analysis"@en, "analyse fonctionnelle"@fr ;
  a skos:Concept ;
  skos:narrower psr:-WLMG00CZ-5 .

psr: a skos:ConceptScheme .