X. Catepillan et W. Szymanski, SEMIGROUP PROPERTIES OF FACTORS IN THE POLAR DECOMPOSITION OR THE OPERATOR DE-MOIVRE FORMULA, Proceedings of the American Mathematical Society, 126(12), 1998, pp. 3521-3526
We give necessary and sufficient conditions under which the factors in
the polar decomposition of a semigroup homomorphism are themselves se
migroup homomorphisms.