then the closure of ⟨ ⟨ E , E ⟩ ⟩ A is a two-sided ideal in A . Two-sided ideals are C*-subalgebras and therefore possess approximate units. One can verify that E ⟨ ⟨ E , E ⟩ ⟩ A is dense in E . In the case when ⟨ ⟨ E , E ⟩ ⟩ A is dense in A , E is said to be full. This does not generally hold.