Worst-case performance conjecture for gradient descent on linear-operator compositions

Let $g$ be a $mu_g$-strongly convex and $L_g$-smooth function, and let $M$ belong to the class of linear operators with singular values in $[mu_M,L_M]$. Write $\mathcal{C}_{mu_g,L_g}^{mu_M,L_M}$ for the corresponding class of functions $F(x)=g(Mx)$, and let $\mathcal{D}_{mu_g,L_g}^{mu_M,L_M}$ denote the analogous class with symmetric $M$. For the worst-case performance $w(\mathcal{F})$ of the gradient method on a class $\mathcal{F}$, measured by the criterion $F(x_N)-F(x^*)$ under $Vert x_0-x^*Vert\backslashleq 1$, the conjecture asserts: Worst-case performance conjecture. For all $0\leq \mu_g\leq L_g$ and $0\leq \mu_M\leq L_M$,

$$w(\mathcal{C}_{\mu_g,L_g}^{\mu_M,L_M})=w(\mathcal{D}_{\mu_g,L_g}^{\mu_M,L_M}).$$

Here $w(\mathcal{D}_{\mu_g,L_g}^{\mu_M,L_M})$ is the expression given in the cited prior conjecture. This conjecture says that the symmetry of the linear operator does not affect the worst-case performance of gradient descent, extending the previously studied zero-minimal-singular-value case; the supplied text does not establish its resolution.