Spectral Theory of Multivalued Linear Operators

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.

Aymen Ammar, PhD, is currently with the Department of Mathematics, Faculty of Sciences of Sfax at the University of Sfax, Tunisia, where he is Assistant Professor. He has published many articles in international journals. His areas of interest include spectral theory, matrice operators, and linear relations.
Aref Jeribi, PhD, is Professor in the Department of Mathematics at the University of Sfax, Tunisia. He has authored several books on spectral theory and applications of linear operators and Banach spaces and Banach algebras. He has also published many journal articles in international journals. His areas of interest include spectral theory, matrice operators, transport theory, Gribov operator, Bargmann space, fixed point theory, Riesz basis, and linear relations.