Some Problems in Operator Theory and Operator Algebras
Jingbo Xia Principal Investigator
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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.