Some Problems in Operator Theory and Operator Algebras

摘要夏 夏将研究某些自同构的全Toeplitz代数所引起的同态的单位圆。 他将研究问题的同时对角化所有的Lipschitz函数在一个给定的度量空间模范数理想的紧凑运营商，和动力系统有关的一类薛定谔运营商。 另一条研究路线涉及各种物理模型中的哈密顿算子。 这方面的一个例子是在分数量子霍尔效应的研究中出现的均匀磁场中的二维库仑相互作用。 作用在Hilbert空间上的线性算子的研究可以看作是线性代数在无穷维空间上的推广。它在偏微分方程、流体动力学和量子力学等领域都有历史渊源和应用。的 夏的工作涉及到某些运营商，从物理上的考虑，并有重要的应用。

Abstract Xia Xia will study certain automorphisms on the full Toeplitz algebra which are induced by homomorphisms of the unit circle. He will study the problem of simultaneously diagonalizing all the Lipschitz functions on a given metric space modulo norm ideals of compact operators, and the dynamical systems related to a class of Schrodinger operators. Another line of research involves Hamiltonian operators in various physical models. One example of this is the two-dimensional Coulmob interactions in a homogeneous magnetic field which arise in the study of fractional quantum Hall effect. The study of linear operators acting on Hilbert spaces can be viewed as an extension of linear algebra to an infinite dimensional setting. It has historical origins and applications in such fields as partial differential equations, fluid dynamics, and quantum mechanics. The work of Xia is concerned with certain operators that arise from physical considerations and have significant application.