On the partial indices of triangular matrix functions with prescribed indices of their diagonal entries (Q1728895)

Given \(\chi=(\chi_1,\chi_2,\dots,\chi_n)\in\mathbb{Z}^n\), let \(T(\chi)\) denote the set of all lower triangular \(n\times n\) matrix functions defined on a Carleson closed curve, with bounded measurable entries, \(L_p\)-factorable diagonal entries, and the fixed tuple \(\chi\) of indices of their diagonal entries. Then all matrix functions \(G\in T(\chi)\) admit right generalized factorization in \(L_p\). An explicit description of all possible right partial indices tuples for all matrix functions \(G\in T(\chi)\) is obtained by applying contractions and majorizations. For the entire collection see [Zbl 1392.45001].