# GeneralizedM-matrices and ordered Banach algebras

- Authors
- Journal
- Linear Algebra and its Applications 0024-3795
- Publisher
- Elsevier
- Publication Date
- Volume
- 363
- Identifiers
- DOI: 10.1016/s0024-3795(02)00552-9
- Keywords
- Disciplines

## Abstract

Abstract A matrix A∈ R n×n is an M-matrix if and only if the mapping x↦− 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 K={x∈ R n:x k⩾0} . One possibility of generalizing M-matrices is to consider qmi linear mappings on R n with respect to other cones K⊆ R n . 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.

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