Abstract. The main purpose of this paper is to present a reducibility result based on a recent theorem of Turovskii on semi-groups of compact quasinilpotent operators. More precisely, we prove that every non-zero triangularizable family of compact operators has a hyperinvariant subspace, and then we present several sufficient conditions for simultaneous triangularization of a family of compact operators together with its commutant. We also give a different proof of Shulman's theorem. The finite-dimensional version of the results is also mentioned and emphasized.

AMS Subject Classification (1991): 47A15, 47D03, 20M20

Keyword(s): Volterra semigroup (algebra), hyperinvariant subspace, Commutant, Triangularization

Received August 10, 1999. (Registered under 2762/2009.)