Casper Goffman

First course in functional analysis

Metric Space: 1.1 Definitions and examples 1.2 Inequalities of Holder and Minkowski 1.3 Examples continued

Approximately continuous transformations

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THE STRUCTURE OF REGULATED FUNCTIONS

spaces 1.4 Examples continued Function spaces 1.5 Convergence and related notions 1.6 Separable space, examples 1.7 Complete space, examples 1.8 Contractions, applications to differential and integral equations 1.9 Completion 1.10 Category, nowhere differentiable continuous functions 1.11 Compactness, continuity 1.12 Equicontinuity, application to differential equations 1.13 Stone-Weierstrass theorems 1.14 Normal families 1.15 Semi-continuity, application to arc length 1.16 Space of compact, convex sets Exercises Banach Spaces: 2.1 Vector space 2.2 Subspace 2.3 Quotient space 2.4 Dimension, Hamel basis 2.5 Algebraic dual, second dual 2.6 Convex sets 2.7 Ordered groups 2.8 Hahn-Banach theorem, separation form 2.9 Hahn-Banach theorem, extension form 2.10 Applications, Banach limits, invariant measure 2.11 Banach space, dual space 2.12 Hahn-Banach theorem in normed space 2.13 Uniform boundedness principle, applications 2.14 Lemma of F. Riesz, applications 2.15 Application to compact transformations 2.16 Applications, weak convergence, summability methods, approximate integration 2.17 Second dual space 2.18 Dual of

Basic sequences in the space of measurable functions

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FUNCTIONS WHOSE FOURIER SERIES CONVERGE FOR EVERY CHANGE OF VARIABLE

2.19 Dual of

Introduction to Functional Analysis.

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And What is Your Erdös Number

, Riesz representation theorem 2.20 Open mapping and closed graph theorems 2.21 Application, projections 2.22 Application, Schauder expansion 2.23 A theorem on operators in

Homeomorphisms in Analysis

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Some Aspects of Fourier Series

Exercises Measure and Integration,

Calculus of several variables

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