ABSTRACT
H. Radjavi [1] proved a very interesting result about irreducible operators. It asserts that each operator on a Hilbert space can be expressed as the sum of two irreducible operators. In this section we will consider a more delicate problem, i.e., is every operator the sum of two (SI) operators? This is a more difficult problem. Up to now, we have only given confirmative answers for some special classes of operators, but we have proved that each operator is the sum of three (SI) operators.
