Generalized M-matrices and ordered Banach algebras Original Research Article

A matrix image is an M-matrix if and only if the mapping xmaps to−Ax is quasimonotone increasing (qmi) and if the right spectral bound of −A is negative. Here qmi is meant with respect to the natural cone image. One possibility of generalizing M-matrices is to consider qmi linear mappings on image with respect to other cones image. We will present results on such mappings in the Banach algebra setting and discuss some special cones. Moreover, by means of one-sided estimates it is possible to get informations on the right spectral bound of qmi mappings.