THE STRONG IRREDUCIBILITY OF A CLASS OF COWEN–DOUGLAS OPERATORS ON BANACH SPACES

Let be the set of Cowen–Douglas operators of index on a nonempty bounded connected open subset of . We consider the strong irreducibility of a class of Cowen–Douglas operators on Banach spaces. We show and give some conditions under which an operator is strongly irreducible. All these results generalise similar results on Hilbert spaces.