Strong Ulam stability of a countable discrete group 
is uniform stability of approximate unitary
representations on all complex Hilbert spaces,
including infinite-dimensional ones. For a map 
with 
, its multiplication defect is
 |
Stability means that for every 
there is a 
such that defect at
most 
implies the existence of a unitary representation 
on the same 
with
 |
The norm is the operator norm, and 
must work for every Hilbert space.
