On the value of the fifth maximal projection constant

Abstract

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 $\lambda (5)\ge 5(11+6\sqrt{5})/59\approx 2.06919$. 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 $\lambda (5)$.

References in corpus (1)

• Mutually unbiased frames

Cited by in corpus (2)

• Putatively optimal projective spherical designs with little apparent symmetry
• Minimal projections onto spaces of polynomials on real euclidean spheres