Mathematics Sciences: Applications of Complete Boundedness to Operator Algebras

小行星9401540 在过去的几年中，算子代数的理论，包括自伴和非自伴都得到了迅速的发展。 许多研究人员最近的发展提供了理论的自伴和非自伴方面之间的进一步联系。拟开展的工作主要集中在算子代数的张量积理论、算子代数的完全有界性、上同调理论及其与代数拓扑的联系。Schur乘子理论，非自伴代数和自伴代数的导子和自同构的结构以及半有限代数中的紧理想扰动也将被研究。 算子理论研究有限矩阵的无限推广。当运算符乘法和加法被定义在运算符集合上时，所得到的集合被称为运算符代数。上同调是一种理论，它考察了局部的碎片何时可以组合在一起形成一个全局的对象。 本项目主要研究算子代数上的上同调。 我们的目标是有助于一个古老的猜想断言，某些上同调的算子代数是平凡的。这意味着局部对象总是可以被拼凑成一个全局对象。 ***

9401540 Smith During the past few years the theory of operator algebras, both selfadjoint and non-selfadjoint has evolved at a rapid pace. Recent developments by many researchers are providing further ties between the selfadjoint and non-selfadjoint aspects of the theory. The proposed work focuses on the theory of tensor products of operator algebras, complete boundedness for operator algebras, cohomology theory, and its connection with algebraic topology. Schur multiplier theory, the structure of derivations and automorphisms of non-selfadjoint and selfadjoint algebras and compact ideal perturbations in semifinite algebras will also be studied. Operator theory is concerned with infinite generalizations of finite matrices. When operator multiplication and addition are defined on a collection of operators the resulting collection is called an operator algebra. Cohomology is a theory that examines when local pieces can be put together to form a global object. This project is concerned with cohomology on operator algebras. The goal is to contribute to an old conjecture which asserts that certain cohomologies of operator algebras are trivial. This would mean that local objects can always be pieced together into a global object. ***