**M3_4P7 FUNCTIONAL ANALYSIS**** **

Syllabus

This course brings together ideas of continuity and linear algebra. It concerns vector spaces with a distance, and involves linear maps; the vector spaces are often spaces of functions. Vector spaces. Existence of a Hamel basis. Normed vector spaces. Banach spaces. Finite dimensional spaces. Isomorphism. Separability. The Hilbert space. The Riesz-Fisher Theorem. The Hahn-Banach Theorem. Principle of Uniform Boundedness. Dual spaces. Operators, compact operators. Hermitian operators and the Spectral Theorem. Extension of the above topics. Banach algebras.

Basic Bibliography

**PROBLEM SETS **

GoTo Problems Sets

**USEFUL LINKS**

Home page for Axiom of Choice

History of Mathematics

*Abstract
linear spaces

*Stefan
Banach

*Life of Stefan
Banach:[Review of Roman Kaluza's 1996 book The Life of Stefan Banach was published in American Mathematical Monthly 104 (1997), 577-579 ]

*
Juliusz Pawel Schauder

*Banach Spaces

*Hahn-Banach Theorem

*Banach-Steinhaus
Theorem

*Banach
Fixed Point Theorem

*Banach-Tarski
paradox

*The
Banach Space Bulletin Board

*Hugo Steinhaus

*Virtual Science Library:
Studia Mathematica 1929-

**What Next???**

PG
Studies at IC: MSc & PhD

**You May Like to Visit **

Pure Mathematics Section

Pure Mathematics MSc

M3P7 Page by Bogus~~l~~aw Zegarlinski : *Comments,
Remarks and Questions Welcome !*