Normed representation of a Banach algebra
= Normed representation of a Banach algebra
{title2=$\pi(A)\subseteq\mathcal B(X)$}
A normed representation acts by individually <bounded operators> on a <normed vector space>. This condition alone does not assume that $a\mapsto\pi(a)$ is <continuous> in the <operator norm>, nor that the representation space is complete. A <continuous> representation has a common bound $\|\pi(a)\|\le C\|a\|$.