Mathematical Sciences: Domains of Derivations

数学科学：推导领域

• 批准号: 9424370
• 负责人: Charles Akemann
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424370&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Domains; Derivations

9424370 Akemann Unbounded derivations of operator algebras have been studied extensively as a model for the infinitesimal time development of a quantum-mechanical system. The proposed research involves a study of unbounded derivations of von Neumann algebras building on Weaver's characterization of the domains of such derivations as Lipschitz algebras, in the commutative case. Operators on a Hilbert space are infinite analogues of finite matrices. They have applications throughout mathematics but the proposed research relates specifically to mathematical physics. Algebras of operators have been used to model certain quantum mechanical systems, particularly those arising in quantum statistical mechanics. The proposal involves a change of the type of operator algebra used in this manner, with the double aim of clarifying the general theory and giving insight into specific examples. ***

9424370算符代数的阿克曼无界导子作为量子力学系统无限小时间发展的模型已被广泛研究。所提出的研究涉及von Neumann代数的无界导子的研究，建立在Weaver对这类导子的域的刻画的基础上，在交换的情况下，如Lipschitz代数。Hilbert空间上的算子是有限矩阵的无限类似。它们在整个数学中都有应用，但拟议的研究特别涉及数学物理。算符代数被用来模拟某些量子力学系统，特别是那些出现在量子统计力学中的系统。该建议涉及改变以这种方式使用的算子代数的类型，具有澄清一般理论和深入了解具体例子的双重目的。***