3 problems

For each dimension $m$, let $\rho_1,\rho_2,\rho_3$ denote the three quantities defined in the paper, and let $\rho(m)$ be the associated complex projection constant. Zauner's conje…

Grünbaum's conjecture. The value $\Pi(X_{_{hex}})=\frac{4}{3}$ is the maximal value of $\Pi(\cdot)$ among two-dimensional Banach spaces; equivalently,

Let $\mathcal{P}_d$ be the space of polynomials of degree at most $d$, and let a minimal projection onto $\mathcal{P}_d$ mean a projection whose operator norm equals the projection…