Generalized Polar Decompositions for Closed Operators in Hilbert Spaces   and Some Applications
  We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators. 
Fritz Gesztesy, Mark Malamud, Marius Mitrea, and Serguei Naboko