Mathematical Sciences: Research on Operators in Hilbert Space

Fialkow教授将研究多元算子理论中关于Hilbert空间中有界线性算子的结构和某些相关C*代数的结构的几个问题。研究的一个方面涉及C*代数中线性方程组的解。另一个方面涉及多项式有界次正规加权移位。最后一个主题是关于算子拟相似的结构和谱不变量的研究。后一种研究特别关注于刻画那些拟类似于单边移位的算子并确定它们的谱性质。希尔伯特空间算子本质上是复数的无限矩阵。这些运算符在应用科学的各个领域都有应用，在纯数学中也是如此。这种类型的研究是对此类物体的某些重要类别进行分类的尝试。

Professor Fialkow will study several questions in multivariable operator theory concerning the structure of bounded linear operators in Hilbert space and the structure of certain associated C* algebras. One aspect of the research concerns the solution of systems of linear equations in C* algebras. Another facet involves polynomially bounded hyponormal weighted shifts. A final topic is the study of structural and spectral invariants for quasisimilarity of operators. The latter research is particularly concerned with characterizing those operators quasisimilar to the unilateral shift and determining their spectral properties. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.