U.S.-Australia Planning Visit: Geometrical Structure and Applications in the Symmetric Non-communtative Spaces of Measurable Operators

美澳规划访问：可测算子对称非交换空间中的几何结构及其应用

• 批准号: 0943485
• 负责人: Anna Kaminska
• 金额: $ 1.02万
• 依托单位: University of Memphis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0943485&HistoricalAwards=false
• 关键词: U.S.; Australia; Planning; Visit; Geometrical

0943485KaminskaThis award supports a planning visit to enable Professor Anna Kaminska at the University of Memphis in Tennessee to meet with Professor Fedor Sukochev at the University of New South Wales in Sydney, Australia and Professor Alan Carey at the Australian National University in Canberra. The visit will help develop a detailed international collaborative research project on isomorphic and isometric geometric properties of (quasi) Banach spaces. They will also include non-commutative operator theory in Hilbert spaces and non-commutative phenomena. The non-commutative spaces are generalization of the unitary ideals to the spaces of measurable operators affiliated to von Neumann algebra with trace, whose singular values lie in a symmetric Banach function space. In recent years they have become subjects of intense studies. During the visit in Sydney, the suggested research topics will be prioritized according to their importance, the degree of difficulties and their promises to be solved. The specific approach to each problem will be discussed and the work will be divided appropriately. There is sufficient overlap of interests between faculty at the University of Memphis (with expertise in symmetric Banach function spaces), the University of New South Wales (with expertise in the non-commutative theory of measurable operators) and the Australian National University (with expertise in non-commutative geometry to indicate that they can successfully pursue the activities proposed, and that the interaction will benefit both sides. In addition, the involvement of a US graduate student from the University of Memphis will enable her to gain a valuable international perspective and insight. She will also participate in discussions on future collaborative activities with the researchers and will present her own research results at an Analysis Seminar at the South Wales University.

0943485卡明斯卡该奖项支持规划访问，使教授安娜卡明斯卡在 田纳西州的孟菲斯大学，与澳大利亚悉尼新南威尔士大学的Fedor Sukochev教授和堪培拉澳大利亚国立大学的Alan Carey教授会面。 这次访问将有助于制定一个详细的国际合作研究项目的同构和等距几何性质的（准）Banach空间。 他们还将包括非交换算子理论在希尔伯特空间和非交换现象。 非交换空间是酉理想在具有迹的von Neumann代数中的可测算子空间的推广，其奇异值位于对称Banach函数空间中. 近年来，它们已成为深入研究的主题。 在悉尼访问期间，建议的研究课题将根据其重要性，困难程度和解决的承诺进行优先排序。 将讨论解决每个问题的具体办法，并适当分工。 在孟菲斯大学（在对称巴拿赫函数空间方面具有专门知识）、新南威尔士大学（在可测算子的非对易理论方面具有专门知识）和澳大利亚国立大学（在非对易几何方面具有专门知识）的教师之间有着充分的利益重叠，这表明他们能够成功地从事所提议的活动，而且这种相互作用将使双方都受益。 此外，来自孟菲斯大学的美国研究生的参与将使她获得宝贵的国际视角和洞察力。 她还将参加与研究人员未来合作活动的讨论，并将在南威尔士大学的分析研讨会上展示自己的研究成果。