The product of operators with closed range
Richard Bouldin · Tohoku Mathematical Journal · 1973
By definition the cosine of the angle between the two subspaces M and iV is sup{|</, g}\:feM, geN, ||/|| = 1= ||0||}.Assuming that A and B are both Hubert space operators with closed range, AB has closed range if and only if the angle between BH and ker An [ker AΠBH]