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arXiv · 2408.13527

The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\log$-algebras

Rustam Abdullaev·Azizkhon Azizov
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Abstract

This paper establishes a necessary and sufficient condition for the coincidence of non-commutative $\log$-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of $\log$-algebras built on non-commutative von Neumann algebras with different exact normal semifinite traces. Additionally, we demonstrate a connection between the isomorphism of non-commutative $\log$-algebras and the isomorphism of the corresponding $\log$-algebras constructed on the center of these von Neumann algebras. Furthermore, we present a necessary and sufficient condition for the isomorphism of $\log$-algebras derived from different von Neumann algebras of type $I_n$.

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Rustam Abdullaev, Azizkhon Azizov. 2024-08-24. The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\log$-algebras. https://arxiv.org/abs/2408.13527

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