Unitary operators in the orthogonal complement of a type I von Neumann algebra in a type II₁ factor

2013/08/03 by Xiaoyan Zhou, Rui Shi, Zhou, Xiaoyan +1
Mathematics · #46L10 #47C15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA #msc:46L10 #msc:47C15

paper · pdf · doi:10.48550/arxiv.1308.0676

11 pages

arxiv created 2013/08/03 · openalex publication_date 2013/08/03 · arxiv updated 2013/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well-known that the equality L_G\ominus L_H=span\L_g:g∈ G-H\^SOT holds for G an i.c.c. group and H a subgroup in G, where L_G and L_H are the corresponding group von Neumann algebras and L_G\ominus L_H is the set \x∈ L_G:E_L_H(x)=0\ with E_L_H the conditional expectation defined from L_G onto L_H. Inspired by this, it is natural to ask whether the equality N\ominus A=span\u: uis unitary inN\ominus A\^SOT holds for N a type II₁ factor and A a von Neumann subalgebra of N. In this paper, we give an affirmative answer to this question for the case A a type I von Neumann algebra.

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