Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research.
- Written in a concise and fluent style
- Covers a broad range of topics
- Includes related topics from research
Table of Contents
1. Introduction and Notations. 2. Linear Topological Spaces. 3. Linear Metric Spaces. 4. Banach Spaces. 5. Hilbert Spaces. 6.Banach Algebras. 7. Measures of Noncompactness. 8. Fredholm Theory. 9. Sequence Spaces. 10. Fixed Point Theory.
Eberhard Malkowsky is a Full Professor at the Department of Mathematics of the Faculty of Sciences at the State University of Novi Pazar in Serbia. He obtained his Ph.D. degree and habilitation at the Department of Mathematics of the Justus-Liebig Universität Giessen in Germany in 1982 and 1988, respectively; the titles of his theses were Toeplitz-Kriterien für Matrizenklassen bei Räumen absolut und stark limitierbarer Folgen, and Matrix Transformations in a New Class of Sequence Spaces that Includes Spaces of Absolutely and Strongly Summable Sequences. He was a visiting professor at several universities in various countries. Furthermore, he participated as an invited or keynote speaker in numerous international scientific conferences and congresses. He is a member of the editorial boards of many journals of international repute. His list of publications contains more than 160 research papers in international journals. He is the author or co-author of five books, and the editor or co-editor of six proceedings of international conferences. He supervised 6 Ph.D. theses and a great number of B.Sc. and M.Sc theses in mathematics. His interests include functional analysis, summability, matrix transformations, measures of noncompactness and operator theory.
Vladimir Rakocevic is a Full Professor at the Department of Mathematics of the Faculty of Sciences and Mathematics at the University of Niš in Serbia, and a Corresponding Member of the Serbian Academy of Sciences and Arts (SANU) in Belgrade, Serbia. He obtained his Ph.D. degree in mathematics at the Faculty of Sciences of Belgrade University, Serbia, in 1984; the title of his thesis was Essential Spectra and Banach Algebras. He was a visiting professor at several universities and scientific institutions in various countries. Furthermore, he participated as an invited or keynote speaker in numerous international scientific conferences and congresses. He is a member of the editorial boards of many journals of international repute. His list of publications contains more than 150 research papers in international journals and he was included in Thomson Reuters’ list of Highly Cited Authors in 2014. He is the author or co-author of five books. He supervised 5 Ph.D., and more than 50 B.Sc. and M.Sc. theses in mathematics. His research interests include functional analysis, fixed point theory, operator theory, linear algebra and summability.