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Linear analysis : an introductory course

Author: Béla Bollobás
Publisher: Cambridge [England] ; New York : Cambridge University Press, 1990.
Series: Cambridge mathematical textbooks.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
This introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have some background in real analysis. The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Béla Bollobás
ISBN: 0521383013 9780521383011 0521387299 9780521387293
OCLC Number: 22887518
Description: xi, 240 pages ; 24 cm.
Contents: Basic inequalities --
Normed spaces and bounded linear operators --
Linear functionals and the Hahn-Banach theorem --
Finite-dimensional normed spaces --
The Baire category theorem and the closed-graph theorem --
Continuous functions on compact spaces and the Stone-Weierstrass theorem --
The contraction-mapping theorem --
Weak topologies and duality --
Euclidean spaces and Hilbert spaces --
Orthonormal systems --
Adjoint operators --
The algebra of bounded linear operators --
Compact operators on Banach spaces --
Compact normal operators --
Fixed-point theorems --
Invariant subspaces.
Series Title: Cambridge mathematical textbooks.
Responsibility: Béla Bollobás.
More information:

Abstract:

This introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have some background in real analysis. The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of finite-dimensional spaces, invariant subspace, fixed-point theorem, and the Bishop-Phelps theorem. An outstanding set of exercises run from the elementary to the challenging.

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