Matrix Analysis and Operator Theory
Edward Poon (Toronto):
Matrix analysis and operator theory
Specific interests include doubly stochastic maps and quantum information theory.
I am particularly interested in using analytic techniques to investigate various properties of matrices, or more generally, operators on a Hilbert space, which can be thought of as infinite-dimensional matrices. Some specific topics I have worked on include preserver problems (characterizing maps on matrices and/or operators which preserve some quantity of interest, such as the determinant, rank, norm, eigenvalues, etc., as well as some sort of structure, such as linearity or multiplication, though much weaker conditions are looked at nowadays) and numerical range (or field of values) and its generalizations (this has a wide variety of applications, such as stability, quantum computing, convergence of numerical algorithms, quantum physics, etc.).