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

该奖项支持田纳西州孟菲斯大学的Anna Kaminska教授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教授的计划访问。这次访问将有助于发展一个关于(拟)Banach空间的同构和等距几何性质的详细的国际合作研究项目。它们还将包括希尔伯特空间中的非对易算子理论和非对易现象。非交换空间是么正理想在具有迹的von Neumann代数上的可测算子空间的推广，其奇异值位于对称的Banach函数空间中。近年来，它们已成为密集研究的对象。在悉尼访问期间，建议的研究课题将根据其重要性、困难程度和承诺解决的情况进行优先排序。将讨论解决每个问题的具体方法，并适当分配工作。孟菲斯大学(擅长对称Banach函数空间)、新南威尔士大学(擅长可测算子的非对易理论)和澳大利亚国立大学(擅长非对易几何，表明他们可以成功地从事所提议的活动)的教职员工之间有足够的兴趣重叠，这种互动将对双方都有利。此外，孟菲斯大学一名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关于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她自己的研究成果。

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.