Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.§Although it remains a very attractive field of pure mathematics, it has also proven to be an indispensable and powerful tool for physicists, engineers and economists involved in research and development, for helping them understand their subject in depth. This book is designed to provide the reader with a solid foundation of almost the entire spectrum of functional analysis, upon which each reader may build their own special structure, tailored to his or her purposes. The only prerequisite is the familiarity with the classical analysis of standard level. The book then provides a smooth but fast-paced systematical passage to the required advanced mathematical level, without sacrificing the mathematical rigor with almost no reference to outside materials to offering also a complete coverage of this discipline. We believe that the latter is one of the unique features of this book. None of the books in literature cover that much material, starting from a rather modest mathematical level. §Functional Analysis will be primarily of interest to graduate students in applied mathematics, in all branches of engineering, in physical and economical sciences and to those working in research and development in industry and research institutes.
