2 papers
math.OA2024
Computing the noncommutative inner rank by means of operator-valued free probability theory
Johannes Hoffmann, Tobias Mai, Roland Speicher
We address the noncommutative version of the Edmonds' problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calcula…
math.OA2024
Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates
Tobias Mai, Roland Speicher
We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a l…