Hiroshi Ando
Abstract
In these notes we give a brief look at elements of Tomita-Takesaki modular theory. Then we extend the ultraproduct construction, an extremely useful idea from model theory, to the setting of type III (nontracial) von Neumann algebras.
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In these notes we give a brief look at elements of Tomita-Takesaki modular theory. Then we extend the ultraproduct construction, an extremely useful idea from model theory, to the setting of type III (nontracial) von Neumann algebras.
Key concepts: Ultraproduct, Tomita–Takesaki theory, Von Neumann architecture, Von Neumann algebra, Affiliated operator, Modular design, Pure mathematics, Mathematics