AbstractThe Yang-Baxter-like matrix equation AXA = XAX is reconsidered, where A is any complex square matrix. A collection of spectral solutions for the unknown square matrix X were previously found. When A is diagonalisable, by applying the mean ergodic theorem we propose numerical methods to calculate those solutions.
We study the asymptotic behaviour of solutions of the Cauchy problem u' = ?n j=1(Aj + A-1 j ) - 2nI_u, u(0) = x as t??, for invertible isometries A1, . . . , An.
Power bounded operators and the mean ergodic theorem for subsequences