Includes bibliographical references (pages 394-395) and index.

Part I. Preliminaries

Vector space and bases

Metric spaces

Part II. Normed linear spaces

Norms and normed spaces

Complete normed spaces

Finite-dimensional normed spaces

Spaces of continuous functions

Completions and the Lebesgue space

Part III. Hilbert spaces

Hilbert spaces

Orthonormal sets and orthonormal bases for Hilbert spaces

Closest points and approximation

Linear maps between normed spaces

Dual spaces and the Riesz representation theorem

The Hilbert adjoint of a linear operator

The spectrum of a bounded linear operator

The spectrum of a bounded linear operator

Compact linear operators

The Hilbert-Schmidt theorem

Application : Sturm-Liouville problems

Part IV. Banach spaces

Dual spaces of Banach spaces

The Hahn-Banach theorem

Some applications of the Hahn-Banach theorem

Convex subsets of Banach Spaces

The principle of uniform boundedness

The open mapping, inverse mapping, and closed graph theorems

Spectral theory for compact operators

Unbounded operators on Hilbert spaces

Reflexives spaces

Weak and weak--convergence