Speaker: Gulnara Abduvalieva
Topic: Fixed-point theorems for noncommutative functions
Abstract: We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix size and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a noncommutative function. As a special case, we prove the corresponding contractive mapping theorem which can be viewed as a generalization of the classical Banach Fixed Point Theorem.