Mathematical Sciences: RUI: Krein Space Representations and Index Theory for Derivations

普赖斯教授将考虑一些问题的理论， 算子代数与半群的指标理论 自同态 在这项工作中，普莱斯教授将继续他的工作 与Jorgensen关于他们的Arveson-Powers指数扩展到 为运算符上的某些导数指定索引的设置 代数 他希望继续与鲍尔斯合作， 分析第二类的生成元扩张的问题 对称无界算子的量子化。 他还将学习 一类算子代数同构不变量， 结构类似于单参数Cuntz族 代数 最后，普莱斯将继续他的计划， 研究课题涉及算子的本科生 代数 Price教授的项目涉及自伴算子 代数 这些物体由希尔伯特空间的族组成 运算符（复数的无限矩阵）具有 有趣的性质：代数是由运算符生成的， 在代数的任何状态下的值都是真实的数。 此属性 使得这些代数对物理学很重要，事实上， 他们学习的原始动机。

Professor Price will consider some questions in the theory of operator algebras related to the index theory for semigroups of endomorphisms. In this work Professor Price will continue his work with Jorgensen on their extension of the Arveson-Powers index to a setting which assigns an index to certain derivations on operator algebras. He expects to continue his work with Powers on a related problem of analyzing the generator extensions of the second quantization of a symmetric unbounded operator. He also will study isomorphism invariants for a class of operator algebras whose structure resembles that of a one parameter family of Cuntz algebras. Finally Price will continue his project of acquainting undergraduates with certain research topics involving operator algebras. Professor Price's project involves self-adjoint operator algebras. These objects consist of families of Hilbert space operators (infinite matrices of complex numbers) which have an interesting property: the algebra is generated by operators whose value in any state on the algebra is a real number. This property makes these algebras important for physics and indeed physics was the original motivation for their study.