Diagonality modulo symmetric spaces in semifinite von Neumann algebras

2024/03/30 by A. F. Ber, Ber, Aleksey, Fedor Sukochev +5
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2404.00259

Abstract

In the study on the diagonality of an n-tuple α=(α(j))_j=1ⁿ of commuting self-adjoint operators modulo a given n-tuple Φ=(J₁,…,J_n) of normed ideals in B(H), Voiculescu introduced the notion of quasicentral modulus k_Φ(α) and proved that α is diagonal modulo (J₁,…,J_n) if and only if k_Φ(α)=0. We prove that the same assertion holds true when B(H) is replaced with a σ-finite semifinite von Neumann algebra M, and J₁,…,J_n are replaced with symmetric spaces E₁(M),…,E_n(M) associated with M.

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