On the value of the fifth maximal projection constant
Let $λ(m)$ denote the maximal absolute projection constant over real $m$-dimensional subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that the only known value of $λ(m)$ for $m>1$ is $λ(2)=4/3$. There is also numerical evidence indicating that $λ(3)=(1+\sqrt{5})/2$. In this paper, relying on a new construction of certain mutually unbiased equiangular tight frames, we show that $λ(5)\geq 5(11+6\sqrt{5})/59 \approx 2.06919$. This value coincides with the numerical estimation of $λ(5)$ obtained by B. L. Chalmers, thus reinforcing the belief that this is the exact value of $λ(5)$.
math.FA↗