The Kadison-Kastler conjecture asks whether operator algebras sufficiently close in Kadison-Kastler
distance must be equivalent, with formulations specifying algebraic isomorphism
or spatial conjugacy. Spatial conjugacy of represented algebras 
means that 
for some unitary
transformation 
. The choice between C*-algebras
and von Neumann algebras is also part of the
formulation.
Kadison-Kastler Conjecture
See also
C*-Algebra, Kadison-Kastler Distance, Near Inclusion of Operator Algebras, von Neumann AlgebraExplore with Wolfram|Alpha
References
Schafhauser, C.; Tikuisis, A.; and White, S. "Nuclear
-Algebras:
99 Problems." 12 Jun 2025. https://arxiv.org/abs/2506.10902.
Cite this as:
Weisstein, Eric W. "Kadison-Kastler Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Kadison-KastlerConjecture.html