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Positivity and its applications : Positivity X, 8-12 July 2019, Pretoria, South Africa / / editors, Eder Kikianty [et al.]
| Positivity and its applications : Positivity X, 8-12 July 2019, Pretoria, South Africa / / editors, Eder Kikianty [et al.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing AG, , 2021 |
| Descrizione fisica | 1 online resource (321 pages) |
| Altri autori (Persone) |
KikiantyEder
MabulaMokhwetha MesserschmidtMiek van der WaltJan Harm WortelMarten |
| Collana | Trends in mathematics |
| Soggetto topico |
Operator theory
Ordered topological spaces Positive operators Teoria d'operadors Espais topològics ordenats |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-70974-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Coenraad Christoffel Andries Labuschagne -- Inverse Monotonicity of Elliptic Operators in Variational Form -- 1 Introduction -- 2 Operators Associated with Elliptic PDEs: The Classical Case -- 3 Operators Associated with Elliptic PDEs in Variational Formulation -- 4 Operators Associated with Weakly Coupled System of PDEs in Variational Form -- 5 Conclusion -- References -- On Compact Operators Between Lattice Normed Spaces -- 1 Introduction -- 2 Preliminaries -- 3 p-Compact Operators Are p-Bounded -- 4 Semicompact Operators -- 5 rp-Compact Operators -- References -- How to Be Positive in Natural Sciences? -- 1 Introduction -- 2 Population Balance Equations -- 3 Finite-Dimensional Population Equation -- 4 Making a Step to Infinity -- 4.1 A Death Equation: Multiple Solutions -- 4.2 A Birth Process: Breach of the Conservation Law -- 5 Between Model and Its Analysis -- 6 Substochastic Semigroup Theory -- 6.1 Generation Theorems -- 6.2 How Do Multiple Solutions Fit into the Theory of Semigroups? -- 6.3 Perturbation Theory for Positive Semigroups -- 7 Honesty of the Semigroup and Characterization of Its Generator -- 7.1 The Three Functionals -- 7.2 Structure of Honesty -- 7.3 A Hunt for Honest Semigroups -- 8 Conclusion -- References -- Real Positive Maps and Conditional Expectations on OperatorAlgebras -- 1 Introduction: Real Positivity -- 2 Some General Results on Real Positivity -- 3 Real Positive Maps -- 4 Quasimultipliers and a Banach-Stone Theorem -- 5 Contractive Projections on Operator Algebras -- 6 What Are Conditional Expectations? -- 7 Noncommutative Characters on Noncommutative Function Algebras (Operator Algebras) -- References -- Free Vector Lattices and Free Vector Lattice Algebras -- 1 Introduction and Overview -- 2 Free Objects -- 3 Universal Algebra: Part I.
4 Various Lattices as Abstract Algebras Satisfying Identities -- 5 Universal Algebra: Part II -- 6 Free Vector Lattices and Free Objects of Categories of Vector Lattice Algebras -- 7 Free Objects Over Lattices -- 8 Free f-algebras -- References -- On Disjointness, Bands and Projections in Partially Ordered Vector Spaces -- 1 Introduction -- 1.1 Disjointness -- 1.2 Disjoint Complements and pre-Riesz Spaces -- 1.3 Organisation of the Paper -- 1.4 Setting the Stage -- 2 Bands -- 2.1 Basics -- 2.2 The Lattice of All Bands -- 2.3 The Sum of Two Bands -- 3 Band Projections -- 3.1 Basics -- 3.2 The Boolean Algebra of Band Projections -- 3.3 The Intersection of Arbitrarily Many Projection Bands -- 3.4 Another Characterisation of Band Projections -- 4 Characterisations of Vector Lattices -- 4.1 Criteria in Terms of One-Dimensional Projection Bands -- 4.2 Criteria in Terms of the Number of Projection Bands -- 4.3 Criteria in the Class of Weakly Pervasive Spaces -- 4.4 Criteria in Terms of Other Concepts of Disjointness -- References -- 101 Years of Vector Lattice Theory: A Vector Lattice-Valued Daniell Integral -- 1 Introduction -- 2 Riesz Spaces or Daniell Spaces? -- 3 Daniell's Paper -- 4 The Vector-Valued I-Integral -- 5 Semi-Integrals -- 6 Summability -- 7 S-Integrals -- 8 Conclusion -- References -- Ergodicity in Riesz Spaces -- 1 Introduction -- 2 Preliminaries -- 3 Ergodicity on Riesz Spaces -- 4 Application to Conditional Weak Mixing -- 5 Application to Processes with Conditionally Independent Shifts -- References -- Multiplicative Representation of Real-Valued bi-Riesz Homomorphisms on Partially Ordered Vector Spaces -- 1 Introduction -- 2 Preliminaries -- 3 Representation of bi-Riesz Homomorphisms -- 4 Kernels of Differences of Riesz Homomorphisms -- References -- Orthogonality: An Antidote to Kadison's Anti-Lattice Theorem -- 1 Introduction. 2 Substitutes for Infimum and Supremum -- 3 Orthogonality and Norm -- References -- Binary Relations in Mathematical Economics: On Continuity, Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot -- 1 Introduction -- 2 Mathematical and Conceptual Preliminaries -- 3 On the Existence of a Continuous Binary Relation -- 3.1 On Ordered Topological Spaces -- 3.2 On Weakly Ordered Topological Spaces -- 3.3 Discussion of the Results -- 4 On the Additivity Postulate -- 4.1 Additivity and Transitivity: A Two-Way Relationship -- 4.2 Implications of Additivity for Monotone Continuity -- 4.3 Discussion of the Results -- 5 Order and Positivity in Mathematical Economics -- References -- On Fixed Point Theory in Partially Ordered (Quasi-)metric Spaces and an Application to Complexity Analysis of Algorithms -- 1 Introduction and Preliminaries -- 2 The Existence of Fixed Point -- 3 The Relationship with Kleene Fixed Point Theorem -- 4 An Application to Complexity Analysis of Algorithms -- 4.1 The Fixed Point Method -- References -- Inheritance Properties of Positive Cones Induced by Subalgebras and Quotients of Ordered Banach Algebras -- 1 Introduction -- 2 Monotonicity of the Spectral Radius -- 3 Normal Algebra Cones -- References -- Universally Complete Spaces of Continuous Functions -- 1 Introduction -- 2 Preliminaries -- 3 Universally Complete C (X) -- References -- Applications of Generalized B*-Algebras to Quantum Mechanics -- 1 Introduction -- 2 Preliminaries -- 3 The Joint System of Quantum Systems -- 4 Quantum Entanglement -- 5 Integral Representations of Positive Linear Functionals of GB*-Algebras and an Alternative Definition of Quantum Entanglement -- 6 Pure States of GB*-Algebras -- 7 Extremal Decomposition of States of Linearly Nuclear *-Algebras -- 8 An Extremal Decomposition Theorem for Locally Convex Quasi *-Algebras. 9 An Example -- References -- List of Participants. |
| Record Nr. | UNINA-9910495154403321 |
| Cham : , : Springer International Publishing AG, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Positivity and its applications : Positivity X, 8-12 July 2019, Pretoria, South Africa / / editors, Eder Kikianty [et al.]
| Positivity and its applications : Positivity X, 8-12 July 2019, Pretoria, South Africa / / editors, Eder Kikianty [et al.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing AG, , 2021 |
| Descrizione fisica | 1 online resource (321 pages) |
| Altri autori (Persone) |
KikiantyEder
MabulaMokhwetha MesserschmidtMiek van der WaltJan Harm WortelMarten |
| Collana | Trends in mathematics |
| Soggetto topico |
Operator theory
Ordered topological spaces Positive operators Teoria d'operadors Espais topològics ordenats |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-70974-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Coenraad Christoffel Andries Labuschagne -- Inverse Monotonicity of Elliptic Operators in Variational Form -- 1 Introduction -- 2 Operators Associated with Elliptic PDEs: The Classical Case -- 3 Operators Associated with Elliptic PDEs in Variational Formulation -- 4 Operators Associated with Weakly Coupled System of PDEs in Variational Form -- 5 Conclusion -- References -- On Compact Operators Between Lattice Normed Spaces -- 1 Introduction -- 2 Preliminaries -- 3 p-Compact Operators Are p-Bounded -- 4 Semicompact Operators -- 5 rp-Compact Operators -- References -- How to Be Positive in Natural Sciences? -- 1 Introduction -- 2 Population Balance Equations -- 3 Finite-Dimensional Population Equation -- 4 Making a Step to Infinity -- 4.1 A Death Equation: Multiple Solutions -- 4.2 A Birth Process: Breach of the Conservation Law -- 5 Between Model and Its Analysis -- 6 Substochastic Semigroup Theory -- 6.1 Generation Theorems -- 6.2 How Do Multiple Solutions Fit into the Theory of Semigroups? -- 6.3 Perturbation Theory for Positive Semigroups -- 7 Honesty of the Semigroup and Characterization of Its Generator -- 7.1 The Three Functionals -- 7.2 Structure of Honesty -- 7.3 A Hunt for Honest Semigroups -- 8 Conclusion -- References -- Real Positive Maps and Conditional Expectations on OperatorAlgebras -- 1 Introduction: Real Positivity -- 2 Some General Results on Real Positivity -- 3 Real Positive Maps -- 4 Quasimultipliers and a Banach-Stone Theorem -- 5 Contractive Projections on Operator Algebras -- 6 What Are Conditional Expectations? -- 7 Noncommutative Characters on Noncommutative Function Algebras (Operator Algebras) -- References -- Free Vector Lattices and Free Vector Lattice Algebras -- 1 Introduction and Overview -- 2 Free Objects -- 3 Universal Algebra: Part I.
4 Various Lattices as Abstract Algebras Satisfying Identities -- 5 Universal Algebra: Part II -- 6 Free Vector Lattices and Free Objects of Categories of Vector Lattice Algebras -- 7 Free Objects Over Lattices -- 8 Free f-algebras -- References -- On Disjointness, Bands and Projections in Partially Ordered Vector Spaces -- 1 Introduction -- 1.1 Disjointness -- 1.2 Disjoint Complements and pre-Riesz Spaces -- 1.3 Organisation of the Paper -- 1.4 Setting the Stage -- 2 Bands -- 2.1 Basics -- 2.2 The Lattice of All Bands -- 2.3 The Sum of Two Bands -- 3 Band Projections -- 3.1 Basics -- 3.2 The Boolean Algebra of Band Projections -- 3.3 The Intersection of Arbitrarily Many Projection Bands -- 3.4 Another Characterisation of Band Projections -- 4 Characterisations of Vector Lattices -- 4.1 Criteria in Terms of One-Dimensional Projection Bands -- 4.2 Criteria in Terms of the Number of Projection Bands -- 4.3 Criteria in the Class of Weakly Pervasive Spaces -- 4.4 Criteria in Terms of Other Concepts of Disjointness -- References -- 101 Years of Vector Lattice Theory: A Vector Lattice-Valued Daniell Integral -- 1 Introduction -- 2 Riesz Spaces or Daniell Spaces? -- 3 Daniell's Paper -- 4 The Vector-Valued I-Integral -- 5 Semi-Integrals -- 6 Summability -- 7 S-Integrals -- 8 Conclusion -- References -- Ergodicity in Riesz Spaces -- 1 Introduction -- 2 Preliminaries -- 3 Ergodicity on Riesz Spaces -- 4 Application to Conditional Weak Mixing -- 5 Application to Processes with Conditionally Independent Shifts -- References -- Multiplicative Representation of Real-Valued bi-Riesz Homomorphisms on Partially Ordered Vector Spaces -- 1 Introduction -- 2 Preliminaries -- 3 Representation of bi-Riesz Homomorphisms -- 4 Kernels of Differences of Riesz Homomorphisms -- References -- Orthogonality: An Antidote to Kadison's Anti-Lattice Theorem -- 1 Introduction. 2 Substitutes for Infimum and Supremum -- 3 Orthogonality and Norm -- References -- Binary Relations in Mathematical Economics: On Continuity, Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot -- 1 Introduction -- 2 Mathematical and Conceptual Preliminaries -- 3 On the Existence of a Continuous Binary Relation -- 3.1 On Ordered Topological Spaces -- 3.2 On Weakly Ordered Topological Spaces -- 3.3 Discussion of the Results -- 4 On the Additivity Postulate -- 4.1 Additivity and Transitivity: A Two-Way Relationship -- 4.2 Implications of Additivity for Monotone Continuity -- 4.3 Discussion of the Results -- 5 Order and Positivity in Mathematical Economics -- References -- On Fixed Point Theory in Partially Ordered (Quasi-)metric Spaces and an Application to Complexity Analysis of Algorithms -- 1 Introduction and Preliminaries -- 2 The Existence of Fixed Point -- 3 The Relationship with Kleene Fixed Point Theorem -- 4 An Application to Complexity Analysis of Algorithms -- 4.1 The Fixed Point Method -- References -- Inheritance Properties of Positive Cones Induced by Subalgebras and Quotients of Ordered Banach Algebras -- 1 Introduction -- 2 Monotonicity of the Spectral Radius -- 3 Normal Algebra Cones -- References -- Universally Complete Spaces of Continuous Functions -- 1 Introduction -- 2 Preliminaries -- 3 Universally Complete C (X) -- References -- Applications of Generalized B*-Algebras to Quantum Mechanics -- 1 Introduction -- 2 Preliminaries -- 3 The Joint System of Quantum Systems -- 4 Quantum Entanglement -- 5 Integral Representations of Positive Linear Functionals of GB*-Algebras and an Alternative Definition of Quantum Entanglement -- 6 Pure States of GB*-Algebras -- 7 Extremal Decomposition of States of Linearly Nuclear *-Algebras -- 8 An Extremal Decomposition Theorem for Locally Convex Quasi *-Algebras. 9 An Example -- References -- List of Participants. |
| Record Nr. | UNISA-996466389903316 |
| Cham : , : Springer International Publishing AG, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||