Maharam traces on von Neumann algebras
Vladimir Chilin, Botir Zakirov
TL;DR
This paper characterizes Maharam traces on von Neumann algebras with complex order complete vector lattice values and establishes a Radon-Nikodym-type theorem for these traces.
Contribution
It provides a full description of Maharam traces on von Neumann algebras and proves a Radon-Nikodym-type theorem specific to these traces.
Findings
Complete description of Maharam traces on von Neumann algebras
Radon-Nikodym-type theorem established for Maharam traces
Advances understanding of traces with vector lattice values
Abstract
Traces on von Neumann algebras with values in complex order complete vector lattices are considered. The full description of these traces is given for the case when is the Maharam trace. The version of Radon-Nikodym-type theorem for Maharam traces is established.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Spectral Theory in Mathematical Physics · Advanced Topics in Algebra