An Introduction to Functional Analysis 1st Edition by James C. Robinson 9781108771580 1108771580

An Introduction to Functional Analysis 1st Edition James C. Robinson – Ebook Instant Download/Delivery ISBN(s): 9780521728393, 0521728398, 9781108771580, 1108771580

Product details:

• ISBN 10: 1108771580
• ISBN 13: 9781108771580
• Author: James C. Robinson

This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert–Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn–Banach theorem, the Krein–Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.

Table contents:

1 Vector Spaces and Bases

2 Metric Spaces

3 Norms and Normed Spaces

4 Complete Normed Spaces

5 Finite-Dimensional Normed Spaces

6 Spaces of Continuous Functions

7 Completions and the Lebesgue Spaces L[sup(p)]([Omega])

8 Hilbert Spaces

9 Orthonormal Sets and Orthonormal Bases for Hilbert Spaces

10 Closest Points and Approximation

11 Linear Maps between Normed Spaces

12 Dual Spaces and the Riesz Representation Theorem

13 The Hilbert Adjoint of a Linear Operator

14 The Spectrum of a Bounded Linear Operator

15 Compact Linear Operators

16 The Hilbert–Schmidt Theorem

17 Application: Sturm–Liouville Problems

18 Dual Spaces of Banach Spaces

19 The Hahn–Banach Theorem

20 Some Applications of the Hahn–Banach Theorem

21 Convex Subsets of Banach Spaces

22 The Principle of Uniform Boundedness

23 The Open Mapping, Inverse Mapping, and Closed Graph Theorems

24 Spectral Theory for Compact Operators

25 Unbounded Operators on Hilbert Spaces

26 Reflexive Spaces

27 Weak and Weak-∗ Convergence

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