On the value of the fifth maximal projection constant - Texas A&M University (TAMU) Scholar

Let $lambda(m)$ 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 $lambda(m)$ for $m>1$ is $lambda(2)=4/3$. There is also numerical evidence indicating that $lambda(3)=(1+sqrt{5})/2$. In this paper, relying on a new construction of certain mutually unbiased equiangular tight frames, we show that $lambda(5)geq 5(11+6sqrt{5})/59 approx 2.06919$. This value coincides with the numerical estimation of $lambda(5)$ obtained by B. L. Chalmers, thus reinforcing the belief that this is the exact value of $lambda(5)$.

On the value of the fifth maximal projection constant Institutional Repository Document