Operators Between Sequence Spaces and Applications

This book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and simplifications of complicated spaces involving these operators. In order to make it self-contained, comprehensive and of interest to a larger mathematical community, the authors have presented necessary concepts with results for advanced research topics. This book is intended for graduate and postgraduate students, teachers and researchers as a basis for further research, advanced lectures and seminars.

Discusses the modern methods in functional analysis and operator theory Links various fields of functional analysis and operator theory Includes rigorous mathematical proofs and recent results and applications of the discussed concepts Appeals to graduate and postgraduate students, teachers, and researchers alike

Autorentext

BRUNO DE MALAFOSSE was Full Professor at the Laboratoire de Mathématiques Appliquées Havrais, Université du Havre, France, until 2009. He has 35 years of teaching experience in most fields of analysis, probability theory, linear algebra and mathematics for informatics. He obtained the Doctorat of 3eme cycle at the Université du Havre Toulouse III, France, in 1980, with a thesis titled "Contribution à l'étude des systèmes infinis". He completed the Habilitation à Diriger des Recherches in 2004 at the Université du Havre, France, with a titled "Sur la théorie des matrices infinies et applications". His research interests include the infinite matrix theory, summability, differential equations, theory of the sum of operators in the nondifferential case, numerical analysis, convergence of a numerical scheme optimization, quasi-Newton method, continuous fractions, spectral theory and sequence spaces. He is a member of the editorial boards of two reputed journals in Serbia and Jordan and a reviewer for the Mathematical Reviews. His list of publications includes 85 research papers published in international journals. He has been a supervisor/examiner for many doctoral theses in France, Algeria and India.

EBERHARD MALKOWSKY is Full Professor at the Faculty of Management, University Union Nikola Tesla, Belgrade, Serbia. He completed his Ph.D. in Mathematics from Giessen University, Germany, in 1983 with the thesis titled "Toeplitz-Kriterien für Matrizenklassen bei Räumen absolut und stark limitierbarer Folgen". He also completed his Habilitation in Mathematics at Giessen University, Germany, in 1989, with the thesis titled "Matrix transformations in a new class of sequence spaces that includes spaces of absolutely and strongly summable sequences". He has 40 years of teaching experience in all fields of analysis, differential geometry and computer science at universities in Germany, South Africa, Serbia, Jordan and Turkey, and as a visiting professor in the USA, India, Hungary, France and Iran. He was also an invited lecturer at four summer schools of the German Academic Exchange Service (DAAD). He has supervised six Ph.D. theses and a number of B.Sc. and M.Sc. theses. His research interests include functional analysis, operator theory, summability, sequence spaces, matrix transformations and measures of noncompactness. He also has developed software for the visualization of topics in mathematics. His list of publications includes 164 research papers, 13 books and proceedings. He is a member of the editorial boards of 10 international journals and a reviewer for the Mathematical Reviews and Zentralblatt der Mathematik. Furthermore, he was the main organizer of 3 and participant of 8 research projects. He was the main organizer and a member of the organizing and scientific committees of 28 international conferences and has delivered more than 100 plenary keynote and invited talks. Moreover, he was an European Union expert for the evaluation of the Tempus Projects from 2004 to 2006.

VLADIMIR RAKOCEVIC is Full Professor at the Department of Mathematics, Faculty of Sciences and Mathematics, University of NiS, Serbia. He is also a corresponding member of the Serbian Academy of Sciences and Arts (SANU) in Belgrade, Serbia. He received his Ph.D. in Mathematics from the Faculty of Sciences, University of Belgrade, Serbia, in 1984; the title of his thesis was "Essential spectra and Banach algebras". His research interests include functional analysis, fixed point theory, operator theory, linear algebra and summability. He was a visiting professor at several universities and scientific institutions across the world. Furthermore, he participated as an invited/keynote speaker at numerous international scientific conferences and congresses. He is a member of the editorial boards of several international journals of repute. His list of publications includes 173 research papers in international journals. He was included in the Thomson Reuter's list of Highly Cited Authors in 2014. He is the co-author of 7 books and has supervised 7 Ph.D. and more than 50 B.Sc. and M.Sc. theses in mathematics.

Inhalt

1. Introduction.- 2. Matrix Domains.- 3. Operators between Matrix Domains.- 4. Statistical Convergence.- 5. Inclusion Equations.- 6. Sequence Space Equations.- 7. Solvability.