Linear Analysis: An Introductory Course

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Cambridge University Press, 04.03.1999 - 240 Seiten
Now revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.
 

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Inhalt

Basic inequalities
1
Normed spaces and bounded linear operators
18
Linear functionals and the HahnBanach theorem
45
Finitedimensional normed spaces
60
The Baire category theorem and the closedgraph theorem
75
Continuous functions on compact spaces and the StoneWeierstrass theorem
85
The contractionmapping theorem
101
Weak topologies and Hilbert spaces
114
Adjoint operators
155
The algebra of bounded linear operators
167
Compact operators on Banach spaces
186
Compact normal operators
198
Fixedpoint theorems
213
Invariant subspaces
226
Index of notation
233
Index of terms
235

Euclidean spaces and Hilbert spaces
130
Orthonormal systems
141

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