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

University Of Memphis, Memphis TN

Investigators

Abstract

0943485 Kaminska This 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.