The non-commutative Yosida-Hewitt decomposition revisited
Peter G. DoddsSchool of Computer Science, Engineering and Mathematics, Flinders University, GPO Box 2100, Adelaide 5001, AustraliaB. de PagterDelft Institute of Applied Mathematics, Faculty EEMCS, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
2012en
ABI
Abstract
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 $\tau$-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.
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Cited by 40 references