Operator and norm inequalities and related topics / / Richard M. Aron [and three others], editors

• Pubblicazione: Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022]; ©2022
• Descrizione fisica: 1 online resource (822 pages)
• Disciplina: 515.724
• Soggetto topico: Operator theory; Inequalities (Mathematics); Desigualtats (Matemàtica); Teoria d'operadors
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): AronRichard M.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Part I: Matrix and Operator Inequalities -- Part II: Orthogonality and Inequalities -- Part III: Inequalities Related to Types of Operators -- Part IV: Inequalities in Various Banach Spaces -- Part V: Inequalities in Commutative and Noncommutative Probability Spaces -- Contents -- Part I Matrix and Operator Inequalities -- Log-majorization Type Inequalities -- 1 Introduction -- 2 Matrix Majorization -- 3 Trace and Determinantal Inequalities -- 4 Golden-Thompson Inequality and Araki's Log-majorization -- 5 Ando-Hiai Inequality -- 6 BLP and Matharu-Aujla Inequalities -- 7 Inequalities for Operator Connections -- 8 Ando and Visick's Inequalities for the Hadamard Product -- 9 Indefinite Inequalities -- References -- Ando-Hiai Inequality: Extensions and Applications -- 1 Introduction -- 2 Extensions -- 3 Applications -- 4 Concluding Remarks -- References -- Relative Operator Entropy -- 1 Introduction -- 2 Operator Means and Solidarities -- 3 Relative Operator Entropy -- 4 CPR Geometry -- 5 Tsallis Relative Entropy -- 6 Concluding Remarks -- References -- Matrix Inequalities and Characterizations of Operator Monotone Functions -- 1 Introduction -- 2 Matrix Inequalities and Characterizations of Operator Functions -- 2.1 Heinz Mean, Heron Mean, and Operator Monotone Functions -- 2.1.1 Scalar Inequality for Heinz Mean and Heron Mean -- 2.1.2 Matrix Inequalities and Operator Monotone Functions -- 2.2 Symmetric and Self-adjoint Means via Integral Representations -- 2.2.1 Symmetric Means -- 2.2.2 Self-adjoint Means -- 2.2.3 Kubo-Ando Condition -- 2.2.4 General Symmetric Means -- 2.3 Matrix Power Means and Operator Monotone Functions -- 2.3.1 Kubo-Ando Matrix Power Means and Characterizations -- 2.3.2 The Inverse Problem for Non-Kubo-Ando Matrix Power Means. ; 3 Powers-Størmer's Inequality and Characterizations of Operator Monotone Functions -- References -- Perspectives, Means and their Inequalities -- 1 Introduction -- 2 Perspectives for Invertible Operators -- 2.1 Homogeneity -- 2.2 Convexity -- 2.3 Monotonicity and Convergence -- 2.3.1 Monotonicity for One Direction -- 2.3.2 Monotonicity for Each Variable -- 3 An Extension of the Perspective Function -- 3.1 A Functional Calculus for Commuting Positive Operators -- 3.2 Pusz-Woronowicz Functional Calculus -- 3.2.1 The Commuting Pair (R,S) -- 3.2.2 Variational Expression -- 3.2.3 Pusz-Woronowicz Functional Calculus -- 3.2.4 Homogeneity, Upper Continuity and Convexity -- 3.2.5 Restricted Domain -- 4 Theory of Operator Means -- 4.1 Kubo-Ando's Axiomatization -- 4.2 Operator Means -- 4.2.1 Integral Representation -- 4.2.2 Geometric Mean -- 4.2.3 Mean of Projections -- 4.2.4 Transforms on OM+1 -- 4.2.5 Weight and Symmetricity -- 4.2.6 Power Means -- 4.2.7 Stolarsky Means -- 4.2.8 Means of Szabó Type -- 5 Operator Inequalities -- 5.1 Positive Maps -- 5.2 Power Monotonicity -- 5.2.1 Ando-Hiai Type Inequalities -- 5.3 Furuta Inequality -- 5.4 Chaotic Order -- 5.5 Notes and Remarks -- References -- Cauchy-Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications -- 1 Introduction -- 2 Cauchy-Schwarz Operator and Norm Inequalities for i.p.t. Transformers -- 3 Aczél-Bellman Type Norm Inequalities for i.p.t. Transformers -- 4 Norm Inequalities for Transformers Generated by Analytic Functions with Non-negative Taylor Coefficients -- 5 Grüss-Landau Type Norm Inequalities for i.p.t. Transformers -- 6 Norm Inequalities for Holomorphic Functions on Simply Connected Domains in the Complex Plane -- 7 Mean Value Norm Inequalities for Operator Monotone Functions and Heinz Inequalities, with Applications. ; 8 Laplace Transformers, Arithmetic-Geometric and Young Norm Inequalities -- 9 Applications to Refinements and Generalizations of Minkowski, Zhan and Heron Inequalities -- 10 Connections with Cauchy-Schwarz Inequalities for Hilbert Modules -- References -- Norm Estimations for the Moore-Penrose Inverse of the Weak Perturbation of Hilbert C*-Module Operators -- 1 Introduction -- 2 Some Basic Knowledge About the Moore-Penrose Inverse -- 3 Various Types of Perturbations -- 3.1 The Multiplicative Perturbation Case -- 3.2 The Stable Additive Perturbation and the Strong Perturbation -- 4 Representations for the Moore-Penrose Inverse -- 5 Norm Estimations for the Moore-Penrose Inverse -- References -- Part II Orthogonality and Inequalities -- Birkhoff-James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs -- 1 Introduction -- 1.1 Roberts Orthogonality -- 1.2 Isosceles Orthogonality -- 1.3 Birkhoff-James Orthogonality -- 1.4 A Plethora of Orthogonalities -- 2 Properties of B-J Orthogonality -- 2.1 Gateaux Derivatives and Complex Case Related to Real Orthogonality -- 2.2 Symmetry, Additivity and Uniqueness of B-J Orthogonality -- 2.3 Mutual B-J Orthogonality -- 3 Examples of B-J Orthogonality -- 3.1 B-J Orthogonality in B(H) and Beyond -- 3.2 B-J Orthogonality in Commutative C*-Algebras and Function Spaces -- 3.3 B-J Orthogonality in General C*-Algebras and Hilbert C*-Modules -- 3.4 Strong B-J Orthogonality on Hilbert C*-Modules -- 4 Applications of B-J Orthogonality -- 5 Preservers of B-J Orthogonality -- 6 Graph Induced by B-J Orthogonality -- 6.1 Property Recognition -- 6.2 Isomorphism Problem -- References -- Approximate Birkhoff-James Orthogonality in Normed Linear Spaces and Related Topics -- 1 Introduction and Preliminaries -- 1.1 Orthogonality in Inner Product Spaces -- 1.2 Orthogonalities in Normed Spaces. ; 2 Approximate Birkhoff-James Orthogonality in Normed Linear Spaces -- 3 Applications and Generalizations-Review of Selected Results -- 3.1 Approximate Birkhoff-James Orthogonality in Operator Theory -- 3.2 Operators Approximately Preserving Orthogonality -- 3.3 Approximate Symmetry of the Birkhoff-James Orthogonality -- 3.4 Varia -- References -- Orthogonally Additive Operators on Vector Lattices -- 1 Introduction -- 2 Definition and Main Examples of OAOs -- 3 The Lateral Order and Related Notions -- 3.1 Basic Properties -- 3.2 Lateral Ideal and Lateral Bands -- 3.3 The Intersection Property -- 4 Extension of Orthogonally Additive Maps -- 5 The Order Structure on the Vector Lattice of OAOs -- 5.1 Order Calculus and Riesz-Kantorovich Types Formulas -- 5.2 The Boolean Algebra of Fragments of a Positive OAO -- 6 Compact Orthogonally Additive Operators -- 6.1 The Projection Band of C-Compact Orthogonally Additive Operators -- 6.2 Domination Problem for AM-Compact Abstract Uryson Operator -- 7 Partial Order Continuities of Orthogonally Additive Operators -- 8 Narrow OAOs and Representation of Regular Operators -- 8.1 Narrow Operators -- 8.2 Representation of Regular Operators -- 9 Banach Lattices of OAOs -- 9.1 Absolute and Uniform Norms of an Abstract Uryson Operator -- 9.2 Consistent Sets and Levels in a Vector Lattice -- 9.3 Linear Sections of Orthogonally Additive Operators -- 10 Open Problems -- 10.1 An Analytic Representation of OAOs -- 10.2 Disjointness Preserving OAOs -- 10.3 Compact OAOs -- 10.4 Order Projections -- 10.5 Partial Order Continuities of Orthogonally Additive Operators -- References -- Part III Inequalities Related to Types of Operators -- Normal Operators and their Generalizations -- 1 Introduction -- 2 Notations and Preliminary Results on Spectral Theory -- 3 Some Notions of Local Spectral Theory -- 4 Normal Type Operators. ; 5 Totally Hereditarily Normaloid Operators -- 6 Weyl Type Theorems for Analytically Quasi THN Operators -- References -- On Wold Type Decomposition for Closed Range Operators -- 1 Introduction -- 1.1 Beurling Theorems for Shift Operators -- 1.1.1 The Hardy Space -- 1.1.2 The Bergman Space -- 1.1.3 The Direchlet Space -- 1.1.4 More on Beurling's Theorem for Hilbert Spaces of Analytic Functions -- 1.2 Beurling's Type Theorem for Left Invertible Operators Close to Isometries -- 2 Regular Operators -- 2.1 Moore-Penrose Generalized Inverse -- 2.2 Some Basic Properties of Regular Operators -- 2.3 Restrictions of Regular Operators -- 3 Wold Type Decomposition for Regular Operators -- 3.1 The Main Results -- 3.2 Applications to Weighted Shifts -- 4 Wold-Type Decomposition for Bi-Regular Operators -- 4.1 First Properties -- 4.2 The Cauchy Dual of a Closed Range Operator -- 4.3 Extended Wold-Type Decomposition -- 5 Some Open Questions -- References -- (Asymmetric) Dual Truncated Toeplitz Operators -- 1 Motivation and Basic Notations -- 2 Restrictions of Multiplication Operators and Its Basic Properties -- 3 Basic Properties of ADTTO -- 4 Intertwining Property for ADTTO -- 5 Other Relations with ADTTO -- 6 A Characterization of ADTTO -- 7 A Brown-Halmos Type Theorem for DTTO -- References -- Boundedness of Toeplitz Operators in Bergman-Type Spaces -- 1 Introduction: The Spaces and Operators -- 2 Toeplitz Operators with Oscillating Symbols -- 3 Toeplitz Operators in Hv∞-Spaces: Introduction -- 4 Toeplitz Operators with Harmonic Symbols in Hv∞(D)-Spaces -- 5 General Result on Multipliers and Toeplitz Operators in Hv∞(D) with Radial Symbols -- 6 Supplementary Results on Toeplitz Operators with Radial Symbols -- References -- Part IV Inequalities in Various Banach Spaces -- Disjointness Preservers and Banach-Stone Theorems -- 1 Introduction. ; 2 Three Classical Theorems.
• Titolo autorizzato: Operator and norm inequalities and related topics
• ISBN: 3-031-02104-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910586596303321
• Lo trovi qui: Univ. Federico II
• Serie: Trends in mathematics.