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دسته بندی: ریاضیات ویرایش: نویسندگان: Richard M. Aron, Mohammad Sal Moslehian, Ilya M. Spitkovsky, Hugo J. Woerdeman سری: Trends in Mathematics ISBN (شابک) : 3031021037, 9783031021039 ناشر: Birkhäuser سال نشر: 2022 تعداد صفحات: 822 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 9 مگابایت
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در صورت تبدیل فایل کتاب Operator and Norm Inequalities and Related Topics به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب نابرابری های عملگر و هنجار و موضوعات مرتبط نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
نابرابریها با کاربردهای مختلف در سایر رشتهها، نقش اصلی
را در ریاضیات بازی میکنند. هدف اصلی این جلد ارائه شده چندین
نابرابری مهم ماتریس، عملگر و هنجار به صورت سیستماتیک و مستقل
است. برخی از روشهای قدرتمند برای ارائه نابرابریهای ریاضی
قابلتوجه در تحلیل تابعی، نظریه عملگرها و زمینههای متعدد در
دهههای اخیر مورد استفاده قرار گرفتهاند.
برخی از فصلها به ارائه مجموعهای از خصوصیات جدید از توابع
یکنواخت عملگر اختصاص داده شده است و برخی دیگر به بررسی
نابرابریهای مرتبط با log- میپردازند. عمدهسازی، آنتروپی عملگر
نسبی و نابرابری آندو-هیایی. چندین فصل بر متعامد بودن
Birkhoff-James و متعامد تقریبی در فضاهای Banach و جبرهای عملگر
مانند جبرهای C* از دیدگاه های تاریخی تا توسعه فعلی متمرکز شده
است.
یک گزارش جامع از کران، فشردگی و محدودیت های عملگرهای Toeplitz
می تواند ارائه شود. در کتاب یافت می شود. علاوه بر این، یک نمای
کلی از قضیه اسقف-فلپس-بولوباس ارائه شده است. پیشرفته ترین
نابرابری های هاردی-لیتل وود در فضاهای دنباله ارائه شده
است.
فصل ها به سبکی خواننده پسند نوشته شده اند و می توان آنها را به
طور مستقل خواند. هر فصل شامل کتابشناسی غنی است. این کتاب برای
استفاده محققین و دانشجویان تحصیلات تکمیلی ریاضیات، فیزیک و
مهندسی در نظر گرفته شده است.
Inequalities play a central role in mathematics with
various applications in other disciplines. The main goal of
this contributed volume is to present several important matrix,
operator, and norm inequalities in a systematic and
self-contained fashion. Some powerful methods are used to
provide significant mathematical inequalities in functional
analysis, operator theory and numerous fields in recent
decades.
Some chapters are devoted to giving a series of new
characterizations of operator monotone functions and some
others explore inequalities connected to log-majorization,
relative operator entropy, and the Ando-Hiai inequality.
Several chapters are focused on Birkhoff–James orthogonality
and approximate orthogonality in Banach spaces and operator
algebras such as C*-algebras from historical perspectives to
current development.
A comprehensive account of the boundedness, compactness, and
restrictions of Toeplitz operators can be found in the book.
Furthermore, an overview of the Bishop-Phelps-Bollobás theorem
is provided. The state-of-the-art of Hardy-Littlewood
inequalities in sequence spaces is given.
The chapters are written in a reader-friendly style and can be
read independently. Each chapter contains a rich bibliography.
This book is intended for use by both researchers and graduate
students of mathematics, physics, and engineering.
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 3 Isomorphism of Disjointness Structure 3.1 -Isomorphisms 3.2 Homeomorphism Associated with a -Isomorphism 3.3 Representation 4 Applications 4.1 Order Isomorphism 4.2 Realcompact Spaces 4.3 Ring Isomorphism and Multiplicative Isomorphism 4.4 Isometry 4.5 Nonvanishing Preservers References The Bishop–Phelps–Bollobás Theorem: An Overview 1 Motivation and Historical Background 2 The Bishop–Phelps–Bollobás Property 2.1 For Operators 2.2 For Some Classes of Operators 2.3 For Multilinear Mappings 2.4 For Homogeneous Polynomials 2.5 For Holomorphic Functions 2.6 For Lipschitz Mappings 2.7 For Numerical Radius 3 Sharpness: The Bishop–Phelps–Bollobás Moduli 4 The Point and Operator Properties 5 The Local Properties 5.1 Local Properties for Operators 5.2 Local Properties for Bilinear Mappings 6 Open Questions 7 Further Research and New (or Recent) Possible Lines 8 Tables for Classical Banach Spaces: A Summary References A New Proof of the Power Weighted Birman–Hardy–RellichInequalities 1 Introduction 2 Power-Weighted Birman–Hardy–Rellich Inequalities 3 Some Generalizations Appendix A: Background for the Vector-Valued Case References An Excursion to Multiplications and Convolutionson Modulation Spaces 1 Introduction 2 Preliminaries 2.1 The Short-Time Fourier Transform 2.2 STFT Projections and a Suitable Twisted Convolution 2.3 Gelfand-Shilov Spaces 2.4 Weight Functions 2.5 Mixed Norm Spaces of Lebesgue Type 2.6 Convolutions and Multiplications for Discrete Lebesgue Spaces 3 Modulation Spaces, Multiplications and Convolutions 3.1 Modulation Spaces 3.2 Multiplications and Convolutions in Modulation Spaces 4 Gabor Products and Modulation Spaces Appendix A: Some Properties of Wiener Amalgam Spaces References The Hardy-Littlewood Inequalities in Sequence Spaces 1 Introduction 2 Preliminary Results 3 Theorem 1.1 for m-Linear Forms 4 Theorem 1.2 for m-Linear Forms 5 Theorem 1.3 for Non-negative m-Linear Forms 6 Theorem 1.4 for m-Linear Forms 7 The Critical and Supercritical Cases 8 On the Constants and Some Final Remarks 9 The Gale-Berlekamp Switching Game References Symmetries of C-algebras and Jordan Morphisms 1 Introduction 2 Wigner Theorem 2.1 Probability Version 2.2 Logical Version 3 Dye Theorem 3.1 Dye Theorem for von Neumann Algebras 3.2 Dye Theorem for AW*-algebras 4 Structure of Abelian Subalgebras 4.1 Abelian C-subalgebras 4.2 Abelian von Neumann Subalgebras 4.3 Abelian Subalgebras as Invariants 5 Choquet Order Structure References Part V Inequalities in Commutative and Noncommutative Probability Spaces Mixed Norm Martingale Hardy Spaces and Applications in Fourier Analysis 1 Introduction 2 Mixed Lebesgue Spaces 3 Doob's Inequality 4 Mixed Martingale Hardy Spaces 5 Atomic Decomposition 6 Martingale Inequalities 7 Dual Spaces of Mixed Hardy Spaces 8 One-dimensional Walsh-Fourier Series 9 Higher Dimensional Walsh-Fourier Series References The First Eigenvalue for Nonlocal Operators 1 Nonlocal Diffusion Problems 2 The First Eigenvalue with Dirichlet or Neumann Boundary Conditions 2.1 Dirichlet Boundary Conditions 2.2 Neumann Boundary Conditions 2.3 Optimal Constants in Lq 2.3.1 The Dirichlet Case 2.3.2 The Neumann Case References Comparing Banach Spaces for Systems of Free Random Variables Followed by the Semicircular Law 1 Introduction 1.1 Background 1.2 Motivation 1.3 Overview 2 Preliminaries 3 Free Distributions of Multi Semicircular Elements 4 A C*-Probability Space Generated by |N|-Many Semicircular Elements 4.1 Free-Isomorphic Relations 4.2 A C*-Probability Space Xφ 5 Free-Distributional Data on Xφ 6 Certain Free-Isomorphisms on Xφ 6.1 Shifts on Z 6.2 Integer Shifts on Xφ 6.3 Free-Isomorphic Relations on Xφ 7 Free Random Variables followed by the Semicircular Law 7.1 Group C*-Algebra of λ 7.2 The Tensor Product C*-Algebra X 7.3 Free-Distributional Information on Xτ 7.4 A Structure Theorem of Xτ 8 Certain Banach-Space Operators Acting on Xτ 8.1 Banach-Space Operators Ts,ltB(Xτ) 8.2 Multiplication Operators Muk0,j0 of B(Xτ) References