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.
Kobos (2026) acknowledges Microsoft Copilot discussions concerning mathematical aspects, while stating that the essential mathematical ideas were not AI-generated.
