representations of Banach *-algebras are continuous

Theorem - Let $\pi :𝒜⟶ℬ(H)$ be a representation (http://planetmath.org/BanachAlgebraRepresentation) of a Banach *-algebra $𝒜$ on a Hilbert space $H$. Then $\pi$ is bounded (http://planetmath.org/BoundedOperator) and $\parallel \pi \parallel \le 1$.

Title	representations of Banach *-algebras are continuous
Canonical name	RepresentationsOfBanachalgebrasAreContinuous
Date of creation	2013-03-22 17:27:41
Last modified on	2013-03-22 17:27:41
Owner	asteroid (17536)
Last modified by	asteroid (17536)
Numerical id	5
Author	asteroid (17536)
Entry type	Theorem
Classification	msc 46K10