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Full Description
This textbook offers an accessible introduction to Functional Analysis, providing a solid foundation for students new to the field. It is designed to support learners with no prior background in the subject and serves as an effective guide for introductory courses, suitable for students in mathematics and other STEM disciplines.
The book provides a comprehensive introduction to the essential topics of Functional Analysis across the first seven chapters, with a particular emphasis on normed vector spaces, Banach spaces, and continuous linear operators. It examines the parallels and distinctions between Functional Analysis and Linear Algebra, highlighting the crucial role of continuity in infinite-dimensional spaces and its implications for complex mathematical problems.
Later chapters broaden the scope, including advanced topics such as topological vector spaces, techniques in Nonlinear Analysis, and key theorems in theory of Banach spaces. Exercises throughout the book reinforce understanding and allow readers to test their grasp of the material.
Designed for students in mathematics and other STEM disciplines, as well as researchers seeking a thorough introduction to Functional Analysis, this book takes a clear and accessible approach. Prerequisites include a strong foundation in analysis in the real line, linear algebra, and basic topology, with helpful references provided for additional consultation.
Contents
Contents.- Preface.- Normed Vector Spaces.- Continuous Linear Operators.- Hahn-Banach Theorems.- Duality and Reflexive Spaces.- Hilbert Spaces.- Weak Topologies.- Spectral Theories of Compact Self-Adjoint Operators.- Topological Vector Spaces.- Introduction to Nonlinear Analysis.- Elements of Banach Space Theory.- A Zorn's Lemma.- B Concepts of General Topology.- C Measure and Integration.- D Answers/hints for selected exercises.- Bibliography.- Index.
