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A simple characterization of commutative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$H*$"><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-algebras
Commutative H * ‐algebras are characterized without postulating the existence of Hilbert space structure.