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Continuous functional calculus
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, particularly in <a href="/facts/Operator_theory/Ays1ofel">operator theory</a> and <a href="/facts/C*-algebra/B3tnGHIo">C*-algebra</a> theory, the continuous functional calculus is a <a href="/facts/Functional_calculus/Y84ugVzS">functional calculus</a> which allows the application of a <a href="/facts/Continuous_function/sKbl02pB">continuous function</a> to <a href="/facts/Normal_element/RHIIdbaQ">normal elements</a> of a C*-algebra. </p><p>In advanced theory, the applications of this functional calculus are so natural that they are often not even mentioned. It is no overstatement to say that the continuous functional calculus makes <i>the</i> difference between C*-algebras and general <a href="/facts/Banach_algebra/3BTHdpg2">Banach algebras</a>, in which only a <a href="/facts/Holomorphic_functional_calculus/xtWI9f4V">holomorphic functional calculus</a> exists. </p>