Mathematical Sciences: Projects in Operator Algebra

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9401174 Muhly Muhly will investigate a range of problems in the structure theory of operator algebras. He will concentrate on the question of how the collection of Hilbert space representations of an operator algebra (or the category of Hilbert modules over the algebra) reflect on the algebra. He will study, too, the structure of operator spaces that are modules over operatoralgebras. Operators can be viewed as infinite dimensional versions of matrices. operators have a natural addition and multiplication and a collection of operators can be consider as a mathematical structure referred to as an operator algebra. These operator algebras can be represented in various explicit manners and Muhly will look at how the various representations reflect on the algebra. He will also study applications of operator algebras to questions of design and control theory. Particular attention will be given to applications to neural networks and to non-stationary control theory that occurs in materials production and noise abatement. ***