An operator in a Banach space is called upper (resp. lower) semi-Browd
er if it is upper (lower) semi-Fredholm and has a finite ascent (resp.
descent). An operator in a Banach space is called semi-Browder if it
is upper semi-Browder or lower semi-Browder. We prove the stability of
the semi-Browder operators under commuting Riesz operator perturbatio
ns. As a corollary we get some results of Grabiner [6], Kaashoek and L
ay [8], Lay [11], Rakocevic [15] and Schechter [16].