Mathematical Sciences: Operator Algebras and Operator Theory

拉尔森教授和史密斯教授将在算子代数的几个领域进行研究。Larson教授将研究巢的相似理论、von Neumann代数中的拟三角性、算子代数的自反性以及算子代数之间的映射等相关问题。Smith教授将重点研究算子代数的张量积理论、C*-代数的完全有界性、上同调理论以及非自伴代数的导数和自同构的结构。每个研究者的工作方面将有助于三角算子代数的核的联合研究。这个研究项目涉及希尔伯特空间算子族，称为代数。希尔伯特空间算子可以被认为是一个无限的复数矩阵。这些对象在纯数学和应用数学的几乎每一个分支中都很重要。将这些具有共同性质的算子集合在一起形成代数是数学中的一个重要主题。

Professors Larson and Smith will conduct research in several areas of operator algebras. Professor Larson will work on problems related to similarity theory for nests, quasitriangularity considerations within von Neumann algebras, reflexivity properties of operator algebras, and to mappings between algebras of operators. Professor Smith will focus on the theory of tensor products of operator algebras, complete boundedness for C*-algebras, cohomology theory, and the structure of derivations and automorphisms of non-selfadjoint algebras. Aspects of each of the investigator's work will contribute to a joint study of nuclearity in triangular operator algebras. This research project concerns families of Hilbert space operators called algebras. A Hilbert space operator can be thought of as an infinite matrix of complex numbers. Such objects are important in almost every branch of pure and applied mathematics. Putting together aggregates of these operators with common qualities to form an algebra is a major theme in mathematics.