FACTORIZATION OF DIAGONALLY DOMINANT OPERATORS ON L1([0,1],X) Academic Article

Let X X be a separable Banach space. It is shown that every diagonally dominant invertible operator on L 1 ( [ 0 , 1 ] , X ) {L_1}([0,,1],,X) can be factored uniquely as a product of an invertible upper triangular operator and an invertible unit lower triangular operator.