The Kadison-Kastler distance between two operator algebras 
is the Hausdorff distance between their closed unit balls in the
operator norm. Writing 
and 
for these balls, it is
 |
It measures two-sided closeness in the given representation. Restricting the approximants to the unit balls distinguishes this distance from the
one-sided near inclusion of operator
algebras. For example, 
. The Kadison-Kastler
conjecture concerns whether sufficiently small distance forces equivalence of
the algebras.
-Algebras:
99 Problems." 12 Jun 2025.