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This textbook on functional analysis offers a short and concise
introduction to the subject. The book is designed in such a way as
to provide a smooth transition between elementary and advanced
topics and its modular structure allows for an easy assimilation of
the content. Starting from a dedicated chapter on the axiom of
choice, subsequent chapters cover Hilbert spaces, linear operators,
functionals and duality, Fourier series, Fourier transform, the
fixed point theorem, Baire categories, the uniform bounded
principle, the open mapping theorem, the closed graph theorem, the
Hahn-Banach theorem, adjoint operators, weak topologies and
reflexivity, operators in Hilbert spaces, spectral theory of
operators in Hilbert spaces, and compactness. Each chapter ends
with workable problems. The book is suitable for graduate students,
but also for advanced undergraduates, in mathematics and physics.
Contents: List of Figures Basic Notation Choice Principles Hilbert
Spaces Completeness, Completion and Dimension Linear Operators
Functionals and Dual Spaces Fourier Series Fourier Transform Fixed
Point Theorem Baire Category Theorem Uniform Boundedness Principle
Open Mapping Theorem Closed Graph Theorem Hahn-Banach Theorem The
Adjoint Operator Weak Topologies and Reflexivity Operators in
Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces
Compactness Bibliography Index
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