Abstract. This paper concerns strongly irreducible decomposition and irreducible decomposition for Cowen--Douglas operators and operator weighted shifts. We characterize strong irreducibility of an operator weighted shift by the Jacobson radical of its commutant. Moreover, we show that every Cowen--Douglas operator and operator weighted shift has uniquely finite irreducible decomposition under unitary equivalence.

AMS Subject Classification (1991): 46H30, 47A10, 47A55, 47A58

Received November 18, 1998, and in revised form July 6, 1999. (Registered under 2760/2009.)