Relations and radicals in abstract lattices and in lattices of subspaces of Banach spaces and ideals of Banach algebras. Amitsur's theory revisited

We refine Amitsur’s theory of radicals in complete lattices and apply the obtained results to the theory of radicals in the lattices of subspaces of Banach spaces and in the lattices of ideals of Banach and C*-algebras and of Banach Lie algebras.