Lattice isomorphisms between projection lattices of von Neumann algebras

被引：13

作者：

Mori, Michiya ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba, Tokyo 1538914, Japan

来源：

FORUM OF MATHEMATICS SIGMA | 2020年 / 8卷

关键词：

RINGS; AUTOMORPHISMS;

D O I：

10.1017/fms.2020.53

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Generalizing von Neumann's result on type II1 von Neumann algebras, I characterise lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, I give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.

引用

页数：19

共 48 条

[21] Von Neumann algebras as complemented subspaces of B(H)
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[28] CLASSIFICATION OF ORDER PRESERVING ISOMORPHISMS BETWEEN ALGEBRAS OF SEMICLASSICAL OPERATORS
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[30] Maps preserving products XY-YX* on von Neumann algebras
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