Accretive matrices and matrix convex functions
Positive definite matrices play an important role in matrix analysis. A more general class is that of accretive matrices. In the past few years, many results for positive matrices have been extended to the accretive matrices. For example, \textit{F. Hansen} [Linear Algebra Appl. 438, No. 11, 4557--4571 (2013; Zbl 1284.26011)] proved that there exists a probability measure such that the monotone function with identity can be represented by a simple integral form. On the basis of that, \textit{Y. Bedrani} et al. [Positivity 25, No. 4, 1601--1629 (2021; Zbl 1480.15021)] defined matrix means of accretive matrices and showed that the matrix monotone function with identity has a similar simple integral representation. In this paper, the authors deal with accretive matrices via two certain classes of matrix convex functions, instead of matrix monotone functions. More specifically, they present new integral representations for certain matrix convex functions of accretive matrices. These formulas are more manageable than the ones written in terms of the Dunford integral. Moreover, they provide Hermite-Hadamard type and Choi type inequalities for such functions.
scientific article; zbMATH DE number 7468851
scientific article