M345P7 FUNCTIONAL ANALYSIS


Office Hours (Room: 6M55 )

M345P6&7 : Mo 15-16 , Tue 13:30-14:30

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

Theorie des Operations Lineares by Stefan Banach

@archive.org

Kreyszig - Introductory Functional Analysis with Applications

Haïm Brezis, Functional analysis, Sobolev spaces, and partial differential equations.






PROBLEM SETS

PS.1, PS.2 , PS.3 , PS.4

Homework.1, H1.Solutions

Homework.2, H2.Solutions

Homework.3,

Comments, Hints, Solutions

PS.1, PS.2solns, PS.3solns, PS.4solns , Apx_4ps_solns

TASKS

T_w.1

T_w.2




NOTES

notes.1, notes.2, , notes.3





SOME LINKS

*
Home page for Axiom of Choice

*Abstract linear spaces

*Banach Spaces

*Hahn-Banach Theorem

*Banach-Steinhaus Theorem

*Banach Fixed Point Theorem

*Banach-Tarski paradox

*The Banach Space Bulletin Board

*Virtual Science Library: Studia Mathematica 1929-

encyclopediaofmath.org


Hilbert XIII@wiki & MathEncyclopedia

Per Enflo : Not every separable Banach space has a Schauder basis.

M.G. Nadkarni and V.S. Sunder
Hamel bases and measurability



Frigyes Riesz

Andrey Kolmogorov







History of Mathematics

*Stefan Banach

Stefan Banach by Hugo Steinhaus

Banach Polish Mathematic Genius_@uTube

*Scottish Book

* Juliusz Pawel Schauder

*Hugo Steinhaus

Albrecht Pietsch , History of Banach Spaces and Linear Operators






Some Lecture Notes

mit_open_courseware

eth~salamon

Hamel Basis

Open Library : Banach Spaces

Classical Banach Spaces I: Sequence Spaces by Joram Lindenstrauss, Lior Tzafriri





Mid-term lecture feedback questions




M345P7 Page by Boguslaw Zegarlinski : Comments, Remarks and Questions Welcome !