Jim Agler is a mathematician who is an emeritus professor at the University of California, San Diego. He is a fellow of the American Mathematical Society since 2016, for "contributions to operator theory and the theory of analytic functions of several complex variables". [1]
He obtained his Ph.D. from the Indiana University Bloomington in 1980 under the supervision of John B. Conway. [2] His thesis was titled Subjordan Operators. [2] The thesis generalizes the notion of a Jordan operator, originally studied by J. W. Helton, which are of the form A + Q where (defined on a Hilbert space over the complex numbers). [3] Restricting this operator to an invariant subspace produces a subjordan operator. All subjordan operators satisfy the equation . [3] The thesis also characterizes all subjordan operators in terms of the C* algebra . [3]
Agler and John E. McCarthy are the authors of the book Pick Interpolation and Hilbert Function Spaces (American Mathematical Society, 2002). [4]
Some efforts to extend the Herglotz representation theorem are described in Classical function theory, Operator Dilation Theory, and Machine Computations on Multiply-Connected Domains. [5]
