Real rank zero of a unital 
-algebra means that its self-adjoint
elements can be approximated in norm by self-adjoint
elements with finite spectrum. For a nonunital algebra,
the definition is applied to its unitization. Matrix algebras provide examples. This
property is a statement about norm approximation, rather than approximation in a
tracial seminorm.
Real Rank Zero
See also
C*-Algebra, Self-Adjoint Element, Uniform Property Gamma, Uniform Tracial UltrapowerExplore with Wolfram|Alpha
References
Blackadar, B. Operator Algebras: Theory of C*-Algebras and von Neumann Algebras. Berlin, Germany: Springer, 2006. https://doi.org/10.1007/3-540-28517-2.Cite this as:
Weisstein, Eric W. "Real Rank Zero." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RealRankZero.html