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Operator ideal
In functional analysis, a branch of mathematics, an operator ideal is a special kind of class of continuous linear operators between Banach spaces. If an operator T {\displaystyle T} belongs to an operator ideal J {\displaystyle {\mathcal {J}}} , then for any operators A {\displaystyle A} and B {\displaystyle B} which can be composed with T {\displaystyle T} as B T A {\displaystyle BTA} , then B T A {\displaystyle BTA} is class J {\displaystyle {\mathcal {J}}} as well. Additionally, in order for J {\displaystyle {\mathcal {J}}} to be an operator ideal, it must contain the class of all finite-rank Banach space operators.
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