2 papers
math.OA2015
Implicit/inverse function theorems for free noncommutative functions
Gulnara Abduvalieva, Dmitry S. Kaliuzhnyi-Verbovetskyi
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these re…
math.FA2012
Fixed point theorems for noncommutative functions
Gulnara Abduvalieva, Dmitry S. Kaliuzhnyi-Verbovetskyi
We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a m…