On $$\mathfrak{L}_{\infty}$$ -Liftings of the Gelfand–Naimark Morphism

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050328

V. A. Mel’nikov

引用次数: 0

Abstract

Let $M$ be a $W^{\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\mathscr{B}(H)$ factors through an $\mathfrak{L}_{\infty}$-space only if $M$ is a finite type $\mathrm{I}$ algebra

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论 $$\mathfrak{L}_{\infty}$ -格尔芬-奈马克态的提升

摘要让 $M$ 是作用于可分离复希尔伯特空间 $H$ 的 $W^{\ast}$- 代数。我们证明，只有当$M$是一个有限类型的$\mathrm{I}$代数时，$M$对$\mathscr{B}(H)$的包含才会通过一个$\mathfrak{L}_\{infty}$空间的因子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.