The polar decomposition theorem for closed multivalued operators

The polar decomposition provides valuable insight into the nature of single-valued operators by expressing them as the product of a partial isometry and a nonnegative operator. Using a result by T. Kato, this article aims to present a general polar decomposition theorem for arbitrary closed linear relations, extending the classical theorem of polar decomposition of single-valued operators to the realm of closed multivalued operators, and to pave the way for its applications.