Mathematical Sciences: Operator Algebras and Operator Theory

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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.