representations of Banach *-algebras are continuous

Theorem - Let $\pi:\mathcal{A}\longrightarrow\mathcal{B}(H)$ be a representation (http://planetmath.org/BanachAlgebraRepresentation) of a Banach *-algebra $\mathcal{A}$ on a Hilbert space $H$. Then $\pi$ is bounded (http://planetmath.org/BoundedOperator) and $\|\pi\|\leq 1$.

Title representations of Banach *-algebras are continuous RepresentationsOfBanachalgebrasAreContinuous 2013-03-22 17:27:41 2013-03-22 17:27:41 asteroid (17536) asteroid (17536) 5 asteroid (17536) Theorem msc 46K10