# Part II - Linear Analysis

## Lectured by J. W. Luk, Michaelmas 2015

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Normed vector spaces
- 1.1 Bounded linear maps
- 1.2 Dual spaces
- 1.3 Adjoint
- 1.4 The double dual
- 1.5 Isomorphism
- 1.6 Finite-dimensional normed vector spaces
- 1.7 Hahn–Banach Theorem
- 2 Baire category theorem
- 3 The topology of C(K)
- 3.1 Normality of compact Hausdorff spaces
- 3.2 Tietze-Urysohn extension theorem
- 3.3 Arzela-Ascoli theorem
- 3.4 Stone–Weierstrass theorem
- 4 Hilbert spaces