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Full Description
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.
Contents
- Part I Matrix and Operator Inequalities. - Log-majorization Type Inequalities. - Ando-Hiai Inequality: Extensions and Applications. - Relative Operator Entropy. - Matrix Inequalities and Characterizations of Operator Monotone Functions. - Perspectives, Means and their Inequalities. - Cauchy-Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications. - Norm Estimations for the Moore-Penrose Inverse of the Weak Perturbation of Hilbert C∗-Module Operators. - Part II Orthogonality and Inequalities. - Birkhoff-James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs. - Approximate Birkhoff-James Orthogonality in Normed Linear Spaces and Related Topics. - Orthogonally Additive Operators on Vector Lattices. - Part III Inequalities Related to Types of Operators. - Normal Operatorsand their Generalizations. - On Wold Type Decomposition for Closed Range Operators. - (Asymmetric) Dual Truncated Toeplitz Operators. - Boundedness of Toeplitz Operators in Bergman-Type Spaces. - Part IV Inequalities in Various Banach Spaces. - Disjointness Preservers and Banach-Stone Theorems. - The Bishop-Phelps-Bollobás Theorem: An Overview. - A New Proof of the Power Weighted Birman-Hardy-Rellich Inequalities. - An Excursion to Multiplications and Convolutions on Modulation Spaces. - The Hardy-Littlewood Inequalities in Sequence Spaces. - Symmetries of C∗-algebras and Jordan Morphisms. - Part V Inequalities in Commutative and Noncommutative Probability Spaces. - Mixed Norm Martingale Hardy Spaces and Applications in Fourier Analysis. - The First Eigenvalue for Nonlocal Operators. - Comparing Banach Spaces for Systems of Free Random Variables Followed by the Semicircular Law.
