Kallol Paul – författare

This book is a self-contained advanced monograph on inequalities involving the numerical radius of bounded linear operators acting on complex Hilbert spaces. The study of numerical range and numerical radius has a long and distinguished history starting from the Rayleigh quotients used in the 19th century to nowadays applications in quantum information theory and quantum computing.

This monograph is intended for use by both researchers and graduate students of mathematics, physics, and engineering who have a basic background in functional analysis and operator theory. The book provides several challenging problems and detailed arguments for the majority of the results. Each chapter ends with some notes about historical views or further extensions of the topics. It contains a bibliography of about 180 items, so it can be used as a reference book including many classical and modern numerical radius inequalities.

This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of Birkhoff–James orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces.