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Essential Ideal

A closed ideal I in a C^*-algebra A is called essential if I has nonzero intersection with every other nonzero closed ideal A or, equivalently, if aI={0} implies a=0 for all a in A (Raeburn and Williams 1998).

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.Raeburn, I. and Williams, D. P. Morita Equivalence and Continuous-Trace C-*-Algebras. Providence, RI: Amer. Math. Soc., 1998.

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Essential Ideal

Cite this as:

Moslehian, Mohammad Sal. "Essential Ideal." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/EssentialIdeal.html

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