On some factorizations of operators

Given two subsets A and B of the algebra of bounded linear operators on a Hilbert space H we denote by AB := {AB : A is an element of A, B is an element of B}. The goal of this article is to describe AB if A and B denote classes of projections, partial isometries, positive (semidefinite) operators, etc. Moreover, fixed T is an element of AB we shall describe (AB)(T) := {(A, B) is an element of A x B : AB = p(1)((AB)(T)) := is an element of A : T = AB for some B is an element of B} and P-2((AB)(T)) is an element of B : T = AB for some A is an element of (C) 2016 Published by Elsevier Inc.