Weak* continuous states on Banach algebras

Abstract

We prove that if a unital Banach algebra $A$ is the dual of a Banach space $\pd{A}$, then the set of weak* continuous states is weak* dense in the set of all states on $A$. Further, weak* continuous states linearly span $\pd{A}$.

5 pages

References in corpus (2)

• Dual operator systems
• Metric characterizations of isometries and of unital operator spaces and systems