A hereditary 
-subalgebra of a 
-algebra 
is a closed 
-subalgebra 
of 
such that 
for all 
and 
, or equivalently if for 
and 
the inequality 
implies 
.
Hereditary C^*-Subalgebra
This entry contributed by Mohammad Sal Moslehian
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References
Murphy, G. J. C*-Algebras and Operator Theory. New York: Academic Press, 1990.Referenced on Wolfram|Alpha
Hereditary C^*-SubalgebraCite this as:
Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Hereditary C^*-Subalgebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HereditaryC-Star-Subalgebra.html