A projection constant 
, in its relative form,
measures the smallest operator norm of a bounded
linear projection from a normed
space 
onto a linear subspace 
:
 |
In a Hilbert space, orthogonal projections onto nonzero closed subspaces have norm 1. General normed spaces need not have norm-one projections onto their hyperplanes.
Kobos (2026) proved that there is a universal constant 
such that, for every integer 
, some 
-dimensional real normed space 
satisfies 
for every hyperplane 
. More generally, for each fixed 
there is 
such that every 
admits such an 
for all subspaces of codimension
from 1 through 
. The constants do not depend on
, but the argument gives no explicit numerical values.
