In this paper, a new approach to the non-commutative Yosida-Hewitt decomposition is presented in the general setting of non-commutative symmetric spaces of τ-measurable operators affiliated with semi-finite von Neumann algebras. The principal theorem permits the systematic study of the spaces of normal and singular functionals in this general setting. These results are used to study the properties of elements of order continuous norm and of absolutely continuous norm.
|Number of pages||33|
|Journal||TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY|
|Publication status||Published - 2012|