Richard M. Aron

Ilya M. Spitkovsky

Hugo J. Woerdeman

Mohammad Sal Moslehian

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.

Operator and Norm Inequalities and Related Topics

This book is intended for a first linear algebra course. The text includes all essential topics in a concise manner and can therefore be fully covered in a one term course. After this course, the student is fully equipped to specialize further in their direction(s) of choice (advanced pure linear algebra, numerical linear algebra, optimization, multivariate statistics, or one of the many other areas of linear algebra applications). Linear Algebra is an exciting area of mathematics that is gaining more and more importance as the world is becoming increasingly digital. It has the following very appealing features: It is a solid axiomatic based mathematical theory that is accessible to a large variety of students. It has a multitude of applications from many different fields, ranging from traditional science and engineering applications to more ‘daily life’ applications (internet searches, guessing consumer preferences, etc.). It easily allows for numerical experimentation through the use of a variety of readily available software (both commercial and open source). This book incorporates all these aspects throughout the whole text with the intended effect that each student can find their own niche in the field. Several suggestions of different software are made. While MATLAB is certainly still a favorite choice, open source programs such as Sage (especially among algebraists) and the Python libraries are increasingly popular. This text guides the student through different programs by providing specific commands.

What you Need to Know

Linear Algebra

Mihály Bakonyi

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.

Hugo J. Woerdeman

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