Uniform algebra

<h2 id="abstract-characterization">Abstract characterization</h2>
<p>If <i>A</i> is a <a href="/facts/Unital_algebra/8T8ulWJb">unital</a> <a href="/facts/Commutative/WaYxJLxd">commutative</a> <a href="/facts/Banach_algebra/3BTHdpg2">Banach algebra</a> such that 
  
    
      
        
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    {\displaystyle ||a^{2}||=||a||^{2}}
  
 for all <i>a</i> in <i>A</i>, then there is a <a href="/facts/Compact_space/d0cgXJH7">compact</a> <a href="/facts/Hausdorff_space/gbKIrusl">Hausdorff</a> <i>X</i> such that <i>A</i> is isomorphic as a Banach algebra to a uniform algebra on <i>X</i>. This result follows from the <a href="/facts/Spectral_radius_formula/j8T2xrLu">spectral radius formula</a> and the <a href="/facts/Gelfand_representation/QV54f7Jm">Gelfand representation</a>.
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<h2 id="notes">Notes</h2>

<ul><li>Gamelin, Theodore W. (2005). <i>Uniform Algebras</i>. American Mathematical Soc. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-8218-4049-8.</li>
<li>Gorin, E.A. (2001) [1994], <a href="https://www.encyclopediaofmath.org/index.php?title=Uniform_algebra&oldid=49068">"Uniform algebra"</a>, <i><a href="/facts/Encyclopedia_of_Mathematics/WC6mGtPm">Encyclopedia of Mathematics</a></i>, <a href="/facts/European_Mathematical_Society/B3h7b672">EMS Press</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>(Gamelin 2005, p. 25) - Gamelin, Theodore W. (2005). Uniform Algebras. American Mathematical Soc. ISBN 978-0-8218-4049-8. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
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Uniform algebra open-in-new

Uniform algebra