Commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein type-theorem

Abstract

A class of commutative Banach algebras which satisfy a BochnerSchoenberg-Eberlein-type inequality is introduced. Commutative <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript asterisk"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo> ∗ </mml:mo> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{C^ * }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -algebras, the disk algebra and the Hardy algebra on the open disk are examples.