{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:25013"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:25013","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators","abstract":"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".","abstract_html":"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".","abstract_has_math":false,"creators":["Kalauch, Anke"],"institution":"Technische Universität Dresden","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Weber, Martin R.","Wnuk, Witold","Chen, Zi Li"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-07-10","date_published":"2006-07-10","updated_at":"2026-07-24T03:58:35Z","subjects":["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"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Weber, Martin R.","Wnuk, Witold","Chen, Zi Li"]},{"key":"dc:creator","label":"Author","values":["Kalauch, Anke"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden","Technische Universität Dresden"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Technische Universität Dresden"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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".","M-Matrizen werden in der numerischen Mathematik vielfältig angewandt. Eine Verallgemeinerung dieser Matrizen sind entsprechende Operatoren auf halbgeordneten normierten Räumen. Bekannte Aussagen aus der Theorie der M-Matrizen werden auf diese Situation übertragen. Für zwei verschiedene Typen von M-Operatoren werden die folgenden Fragen behandelt: 1. Für welche geordneten normierten Räume sind die beiden Typen gleich? Dies führt zur Untersuchung außerdiagonal-positiver Operatoren. 2. Welche Bedingungen an einen M-Operator sichern, dass seine (positive) Inverse gewissen Maximumprinzipien genügt? Es werden Verallgemeinerungen des "Maximumprinzips für inverse Spalteneinträge" angegeben und untersucht."]},{"key":"dc:title","label":"Title","values":["Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators"]}]}],"canonical_facts":{"dc:contributor":["Weber, Martin R.","Wnuk, Witold","Chen, Zi Li"],"dc:creator":["Kalauch, Anke"],"dc:description.abstract":["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".","M-Matrizen werden in der numerischen Mathematik vielfältig angewandt. Eine Verallgemeinerung dieser Matrizen sind entsprechende Operatoren auf halbgeordneten normierten Räumen. Bekannte Aussagen aus der Theorie der M-Matrizen werden auf diese Situation übertragen. Für zwei verschiedene Typen von M-Operatoren werden die folgenden Fragen behandelt: 1. Für welche geordneten normierten Räume sind die beiden Typen gleich? Dies führt zur Untersuchung außerdiagonal-positiver Operatoren. 2. Welche Bedingungen an einen M-Operator sichern, dass seine (positive) Inverse gewissen Maximumprinzipien genügt? Es werden Verallgemeinerungen des "Maximumprinzips für inverse Spalteneinträge" angegeben und untersucht."],"dc:publisher":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden","Technische Universität Dresden"],"dc:subject":["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"],"dc:title":["Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Technische Universität Dresden"]},"updated_at":"2026-07-24T03:58:35Z"}