= Norm maximum principle for a Banach-space-valued holomorphic function
{title2=$\|f(z)\|\le\sup_{w\in\partial K}\|f(w)\|$}
For a <compact> set $K$ in the domain, a norming <bounded linear functional> at $f(z)$ reduces the assertion to the scalar <maximum modulus principle>. If $z$ lies inside $K$, use its <connected> component of the <interior>; that component's <boundary> lies in $\partial K$. If $z\in\partial K$, the inequality is immediate. No smoothness or connectedness assumption on $K$ is required.
Back to article page
