Operator Norm

Let $V$ be a \reftext{def:vector-space-2026a}{complex vector space} equipped with a \reftext{def:complex-normed-space-2026a}{norm} $\lVert\cdot\rVert$, let $T$ be a \reftext{def:bounded-linear-operator-2026a}{bounded linear operator} on $V$, and let $c$ be a \reftext{def:real-numbers-c54-2026c}{real number}.

The number $c$ is \textbf{an operator norm} of $T$ if $c$ is a \reftext{def:bounded-linear-operator-2026a}{bound} for $T$ and

the order being that of the \reftext{def:ordered-field-c54-2026b}{ordered field} of real numbers.