Necessary and sufficient conditions for $n$-times Fréchet differentiability on ${\mathcal{S}}^p,$ $1<p<\infty .$

Christian Le Merdy, Edward McDonald

Let $1<p<\infty$ and let $n\ge 1$. It is proved that a function $f:\mathbb{R}\to \mathbb{C}$ is $n$-times Fréchet differentiable on ${\mathcal{S}}^p$ at every self-adjoint operat…