Functional analysis, Vol. 1, a gentle introduction / Dzung Minh Ha

This book is an introduction to basics of functional analysis at the undergraduate level. The prerequisites are elementary linear algebra and first-year calculus. In the Preface, the author writes: “Textbooks in functional analysis (or more generally, in mathematics) are often unnecessarily demanding – written in a concise manner with few examples and motivations. [⋯] I chose to write a textbook that I would like to have studied from as a student – one that is mathematically rigorous but leisurely, with lots of motivations and examples." The book discusses standard topics such as metric spaces and normed linear spaces and operators on them with rudiments of topological spaces and topological vector spaces, Banach's fixed point theorem, compactness, results centering around the Baire category theorem, integral operators, inner product spaces and Hilbert spaces. It also includes special topics as the theorems of Korovkin and Bernstein, the Stone–Weierstrass theorem, the Baire–Osgood theorem, Gram determinants, the Müntz theorem and some basic results in the theory of differential equations. The Hahn–Banach theorem is not discussed... (Zentralblatt)

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