Linear Analysis

✍ Scribed by J. W. Luk, ed. Dexter Chua

• Publisher: University of Cambridge
• Year: 2015
• Tongue: English
• Leaves: 78
• Series: Cambridge Mathematical Tripos Part II Lecture Notes
• Category: Library

✦ Table of Contents

Introduction
Normed vector spaces
Bounded linear maps
Dual spaces
Adjoint
The double dual
Isomorphism
Finite-dimensional normed vector spaces
Hahn–Banach Theorem
Baire category theorem
The Baire category theorem
Some applications
The topology of C(K)
Normality of compact Hausdorff spaces
Tietze-Urysohn extension theorem
Arzela-Ascoli theorem
Stone–Weierstrass theorem
Hilbert spaces
Inner product spaces
Riesz representation theorem
Orthonormal systems and basis
The isomorphism with l2
Operators
Self-adjoint operators

✦ Subjects

maths; mathematics; math; advanced; college; university; higher; further; pure; applied; analysis; linear algebra