Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators

M-matrices are extensively employed in numerical analysis. These matrices can be generalized by corresponding operators on a partially ordered normed space. We extend results which are well-known for M-matrices to this more general setting. We investigate two different notions of an M-operator, where we focus on two questions: 1. For which types of partially ordered normed spaces do the both notions coincide? This leads to the study of positive-off-diagonal operators. 2. Which conditions on an M-operator ensure that its (positive) inverse satisfies certain maximum principles? We deal with generalizations of the "maximum principle for inverse column entries".

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Technische Universität Dresden

Year

2006

Author dc:creator

• Kalauch, Anke

Contributors dc:contributor

• Weber, Martin R.
• Wnuk, Witold
• Chen, Zi Li

• Banach lattice
• Cone
• Maximum principle for inverse column entries
• M-matrix
• M-operator
• Partially ordered vector space
• Positive-off-diagonal operator
• Riesz decomposition property
• Außerdiagonal-positiver Operator
• Banach-Verband
• Halbgeordneter Vektorraum
• Kegel
• Maximumprinzip für inverse Spalteneinträge
• Rieszsche Zerlegungseigenschaft