The Semigroup of Normal Singular Operators

Given a group G of invertible operators on a locally convex Hausdorff space X and a continuous projection p on X satisfying [a, p] = ap - pa compact, we set S(G, p) = {ap+ bq + t: a, b ε G, t ε K(X)}, where q = 1-p and K(X) is the set of all compact operators on X(cf [7], Section III. 2.1).