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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
  • Quasimonotonicity
  • Exponential Positivity
  • Banach Algebras
Disciplines
  • Mathematics

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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