Strongly irreducible operators and Cowen-Douglas operators on c 0, l p (1 ⩽ p ∞)

摘要

This paper gives some sufficient conditions for the strongly irreducibility of operators which have the forms of upper triangular operator matrices on Banach spaces. Based on these results, strongly irreducible Cowen-Douglas operators of index n are constructed on c 0, l p (1 ⩽ p ∞) for all 1 ⩽ n ⩽ ∞.