Advanced Techniques with Block Matrices of Operators / by Mohammad Sal Moslehian, Hiroyuki Osaka.

Format:

Book

Author/Creator:

Moslehian, Mohammad Sal, 1966- author.

Osaka, Hiroyuki, author.

Series:

Frontiers in Mathematics, 1660-8054

Language:

English

Subjects (All):

Operator theory.

Operator Theory.

Local Subjects:

Operator Theory.

Physical Description:

1 online resource (226 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.

Summary:

This book introduces several powerful techniques and fundamental ideas involving block matrices of operators, as well as matrices with elements in a C*-algebra. These techniques allow for the solution of problems that may be difficult to treat. Specifically, 2×2 operator matrices yield significant mathematical inequalities in various fields of operator theory and matrix analysis. The authors employ block matrices to simplify complicated problems. Operator matrices have garnered attention for their applications in quantum information and computing theories. Each chapter concludes with a diverse set of exercises and problems for readers, along with references to relevant literature. Some problems pose open questions, while others challenge readers and provide suggestions for future research. This book is suitable for an advanced undergraduate or graduate course and can be used in the classroom. It also serves as a valuable resource for researchers and students in mathematics and physics who have a basic understanding of linear algebra, functional analysis, and operator theory.

Contents:

Preface

1 Matrices and Hilbert Space Operators

2 Block Matrices of Operators

3 Operator Monotone Functions and Positive Maps

4 Operator Variance and Covariance

5 Nonlinear Positive Maps

Bibliography.

Notes:

Includes bibliographical references and index.

ISBN:

3-031-64546-4