Lieb functions and sectorial matrices

In this article, we present a special treatment of sectorial matrices under Lieb functions. This treatment results from a new characterization of sectorial matrices using blocks, which then implies a new set of inequalities governing such matrices, where singular values, determinants, numerical radius and unitarily invariant norms inequalities are retrieved in a general form that implies many well known results in the literature. (C) 2019 Elsevier Inc. All rights reserved.