On maximal relative projection constants Academic Article uri icon


  • 2016 Elsevier Inc. This article focuses on the maximum of relative projection constants over all m-dimensional subspaces of the N-dimensional coordinate space equipped with the max-norm. This quantity, called maximal relative projection constant, is studied in parallel with a lower bound, dubbed quasimaximal relative projection constant. Exploiting alternative expressions for these quantities, we show how they can be computed when N is small and how to reverse the KadecSnobar inequality when N does not tend to infinity. Precisely, we first prove that the (quasi)maximal relative projection constant can be lower-bounded by cm, with c arbitrarily close to one, when N is superlinear in m. The main ingredient is a connection with equiangular tight frames. By using the semicircle law, we then prove that the lower bound cm holds with c<1 when N is linear in m.

published proceedings


author list (cited authors)

  • Foucart, S., & Skrzypek, L.

citation count

  • 8

complete list of authors

  • Foucart, Simon||Skrzypek, Leslaw

publication date

  • January 2017