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
FiguresBasic NotationChoice PrinciplesHilbert SpacesCompleteness Completion and
DimensionLinear OperatorsFunctionals and Dual SpacesFourier SeriesFourier TransformFixed Point
TheoremBaire Category TheoremUniform Boundedness PrincipleOpen Mapping TheoremClosed Graph
TheoremHahn-Banach TheoremThe Adjoint OperatorWeak Topologies and ReflexivityOperators in
Hilbert SpacesSpectral Theory of Operators on Hilbert SpacesCompactnessBibliographyIndex
