Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic inequalities
- 2 Normed spaces and bounded linear operators
- 3 Linear functionals and the Hahn–Banach theorem
- 4 Finite-dimensional normed spaces
- 5 The Baire category theorem and the closed-graph theorem
- 6 Continuous functions on compact spaces and the Stone–Weierstrass theorem
- 7 The contraction-mapping theorem
- 8 Weak topologies and duality
- 9 Euclidean spaces and Hilbert spaces
- 10 Orthonormal systems
- 11 Adjoint operators
- 12 The algebra of bounded linear operators
- 13 Compact operators on Banach spaces
- 14 Compact normal operators
- 15 Fixed-point theorems
- 16 Invariant subspaces
- Index of notation
- Index of terms
7 - The contraction-mapping theorem
Published online by Cambridge University Press: 05 June 2012
Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic inequalities
- 2 Normed spaces and bounded linear operators
- 3 Linear functionals and the Hahn–Banach theorem
- 4 Finite-dimensional normed spaces
- 5 The Baire category theorem and the closed-graph theorem
- 6 Continuous functions on compact spaces and the Stone–Weierstrass theorem
- 7 The contraction-mapping theorem
- 8 Weak topologies and duality
- 9 Euclidean spaces and Hilbert spaces
- 10 Orthonormal systems
- 11 Adjoint operators
- 12 The algebra of bounded linear operators
- 13 Compact operators on Banach spaces
- 14 Compact normal operators
- 15 Fixed-point theorems
- 16 Invariant subspaces
- Index of notation
- Index of terms
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- Linear AnalysisAn Introductory Course, pp. 101 - 113Publisher: Cambridge University PressPrint publication year: 1999