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


GoTo Problems Sets


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-

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