Abstract. A generalization of Turovskii's results for Volterra semigroups to locally convex spaces and some consequences are given.

AMS Subject Classification (1991): 47A15, 47B99, 46A32

Keyword(s): Locally convex space, compact operator, quasinilpotent operator, operator semigroup, invariant subspace, triangularization

Received March 12, 2003, and in final form January 26, 2004. (Registered under 5814/2009.)