Operator norm duality
= Operator norm duality
{title2=$\|A\|=\|A^*\|$}
For bounded operators between <Hilbert spaces>, write the norm as the supremum of $|\langle Ax,y\rangle|$ over unit vectors $x,y$. Moving the operator to the other slot proves equality of its norm with that of its <adjoint operator>. Applied to the exponential matrix, this makes the primal and dual <analytic large sieve inequalities> equivalent.