A C*-algebra character is a nonzero star-homomorphism
from a complex C*-algebra to
. On a unital algebra a
character is automatically unital. For example, evaluation at a point
is a character on the algebra of continuous
complex functions on a compact
space. The matrix algebra 
has no characters for 
.
The absence of characters in a norm central
sequence algebra is the hypothesis of the character criterion for Jiang-Su
stability.
C^*-Algebra Character
See also
C*-Algebra, Dimension-Drop Algebra, Jiang-Su Stability, Norm Central Sequence Algebra, Star-HomomorphismExplore 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. "C^*-Algebra Character." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/C-Star-AlgebraCharacter.html