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
Explore with Wolfram|Alpha
WolframAlpha
More things to try:
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.Referenced on Wolfram|Alpha
Essential IdealCite this as:
Moslehian, Mohammad Sal. "Essential Ideal." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/EssentialIdeal.html