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Linear Analysis

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Author(s): J. W. Luk, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part II Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; analysis; linear algebra

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