Let 
be a 
-algebra.
A 
-subalgebra
(that is a closed 
-subalgebra) 
of 
is called hereditary if 
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.Cite this as:
Moslehian, Mohammad Sal. "Hereditary C^*-Subalgebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HereditaryC-Star-Subalgebra.html