Professor McCarthy's research project will cover a number of areas in Hilbert space operator theory and complex analysis: (a) He will extend some aspects of the theory of Toeplitz operators to the setting of logmodular algebras. (b) He will investigate the boundedness of Toeplitz operators on Hilbert spaces of analytic functions. (c) He will study questions dealing with Toeplitz operators in several complex variables. 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 families of such objects.
