On maximal relative projection constants Academic Article

abstract

• 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.

authors

• Foucart, Simon

published proceedings

• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

author list (cited authors)

• Foucart, S., & Skrzypek, L.

citation count

• 8

complete list of authors

• Foucart, Simon||Skrzypek, Leslaw

publication date

• January 2017

publisher

• Elsevier  Publisher

published in

• Journal of Mathematical Analysis and Applications  Journal

keywords

• Equiangular Lines
• Graphs
• Projection Constants
• Seidel Matrices
• Semicircle Law
• Tight Frames

Digital Object Identifier (DOI)

• 10.1016/j.jmaa.2016.09.066

start page

• 309

end page

• 328

volume

• 447

issue

• 1

URL

• http://dx.doi.org/10.1016/j.jmaa.2016.09.066