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

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

altmetric score

  • 0.25

author list (cited authors)

  • Dergowska, B., Fickus, M., Foucart, S., & Lewandowska, B.

citation count

  • 0

complete list of authors

  • Der╚ęgowska, Beata||Fickus, Matthew||Foucart, Simon||Lewandowska, Barbara

Book Title

  • arXiv

publication date

  • June 2022