Jim Agler

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 ${\displaystyle A^{*}=A,Q^{2}=0,AQ=QA}$ (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 ${\displaystyle {T^{*}}^{3}-3{T^{*}}^{2}T+3T^{*}T^{2}-T^{3}=0}$ .^[3] The thesis also characterizes all subjordan operators in terms of the C* algebra ${\displaystyle \mathbb {C} (I,M_{2}(\mathbb {C} ))}$.^[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]

References

1. "List of Fellows of the American Mathematical Society". ams.org. Retrieved 2016-05-22.
2. Jim Agler at the Mathematics Genealogy Project
3. Agler, Jim (August 1980). Subjordan Operators (Thesis). Indiana University. Retrieved 30 November 2025.
4. "Pick Interpolation and Hilbert Function Spaces | European Mathematical Society".
5. Jim Agler, John Harland, and Benjamin J. Raphael (2008) Classical Function Theory, Operator Dilation Theory, and Machine Computations on Multiply-Connected Domains, Memoirs of the American Mathematical Society #892, ISSN 0065-9266

External links

• http://www.math.ucsd.edu/~jagler/pdf/Curriculum%20Vitae.pdf