FACTORIZATION OF TRIANGULAR OPERATORS AND IDEALS THROUGH THE DIAGONAL

We give a necessary and sufficient condition to determine when an oper ator in the nest algebra of doubly infinite block upper triangular ope rators factors through a diagonal projection. An example shows that th is condition does not extend to more general nest algebras, but a simi lar criterion yields a description of the ideals of nest algebras gene rated by diagonal projections.