A characterization of nonunital operator algebras
A characterization of nonunital operator algebras
We give an abstract matrix norm characterization for operator algebras with contractive approximate identities by using the second dual approach. We show that if <italic>A</italic> is an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript normal infinity"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{L^\infty }</mml:annotation> …