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Hereditary C^*-Subalgebra


Let A be a C^*-algebra. A C^*-subalgebra (that is a closed *-subalgebra) B of A is called hereditary if bab^' in B for all b,b^' in B and a in A, or equivalently if for a in A_+ and b in B_+ the inequality a<=b implies a in B.


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

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