Introduction to Functional Analysis Part III, Autumn 2004

Introduction to Functional Analysis Part III, Autumn 2004

Introduction to Functional Analysis Part III, Autumn 2004

This note covers the following topics: Baire category, Non-existence of
functions of several variables, The principle of uniform boundedness, Zorn's
lemma and Tychonov's theorem, The Hahn-Banach theorem, Banach algebras, Maximal
ideals, Analytic functions, The Gelfand representation.

This PDF book covers the
following topics related to Functional Analysis : The Axiom of Choice and Zorn’s
Lemma, Banach Spaces, Banach algebras and the Stone-Weierstrass Theorem, Hilbert
Spaces, Linear Operators, Duality, Spectral Theory.

Author(s): Daniel Daners, School of
Mathematics and Statistics, University of Sydney

Functional analysis plays an important
role in the applied sciences as well as in mathematics itself. These notes are intended to familiarize the student with the basic
concepts, principles andmethods of functional analysis and its applications, and
they are intended for senior undergraduate or beginning graduate students.
Topics covered includes: Normed and Banach spaces, Continuous maps,
Differentiation, Geometry of inner product spaces , Compact operators and
Approximation of compact operators.

This
note covers the following topics related to functional analysis: Normed Spaces, Linear Operators, Dual Spaces, Normed Algebras, Invertibility,
Characters and Maximal Ideals.