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This paper is a part of a series dealing with subspaces of de Branges spaces of entire functions generated by majorization on subsets of the closed up- per half-plane. In the present, third, part we continue our study of a certain Banach space generated by an admissible majorant. The main theme is "invariance of the unit ball with respect to division by Blaschke products". In connection with this topic representability by means of spe- cial types of majorants plays an important role. We obtain some (positive and negative) results on invariance when dividing by Blaschke factors, and characterize those unit balls representable by log-superharmonic ma- jorants.

Majorization in de Branges spaces. III. Division by Blaschke products