Böcker av Aymen Ammar

This book is based on the theory of nonlinear (Lipschitz) operators. Recently, Lipschitz versions of different types of linear operators were investigated in several papers, as summability, ideals, convexity, and compacteness of Lipschits operators. There are not many books exclusively dealing with the propertie of nonlinear operators as: summability and ideals theory of nonlinear operators.In this book we present the theory of summability of Lipschitz operators, also some properties of linear operators which generalized to Lipschitz operatorsn their excellent book Framer and Johnson have introduce the theory of summability Lipschitz operators between pointed metric spaces and showed that it is a good generalization of the concept of linear p-summing operators between Banach spaces. This work marked the beginning of the theory of generalization of properties of linear operators to nonlinear case. Even in this much simpler case it becomes clear that we cannot hope to get n complete description of all properties of linear operators which generalized to Lipschitz operators. Therefore, we must limit ourselves to particular the dirent notions of Lipschitz operators which exists.

The concept of multivalued linear operators-or linear relations-is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators.The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations.The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

Focuses on the theory of multivalued linear operators, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators, specifically the study of linear relations over real or complex Banach spaces.