Algebraically irreducible representation of a Banach algebra
= Algebraically irreducible representation of a Banach algebra
= Strictly irreducible representation of a Banach algebra
{synonym}
Algebraic irreducibility excludes every proper nonzero invariant <vector subspace>, including those that are not <closed>. It is stronger than topological irreducibility, which excludes only <closed> <invariant subspaces>. For a nonzero irreducible action, every nonzero <vector> is cyclic in the algebraic sense: $A\xi=X$.