Lower norm of an operator
= Lower norm of an operator
{title2=$\nu(T)$}
For a densely defined operator,
$$
\nu(T)=\inf\{\lVert Tx\rVert:x\in D(T),\ \lVert x\rVert=1\}.
$$
The symmetric lower norm $\mu(T)=\min\{\nu(T),\nu(T^*)\}$ equals $\lVert T^{-1}\rVert^{-1}$ when $T$ is invertible and is zero otherwise.
= Lower norm
{synonym}