Analysis in Vector Spaces

All proofs have been written with the student reader in mind.  In each proof, the notation and methods have been chosen to maximize clarity and transparency.

A large number of examples are included to reinforce new concepts and to illustrate how a result or technique can be applied to additional problems.  Counter-examples are also given throughout the book to warn the students against possible mistakes in the subject.

The book is self-contained, and the background material in the first few chapters is sufficient to enable well-motivated students to read the book without undue difficulties. 

To avoid possible ambiguities and misunderstandings, terminology and notation are carefully defined before being used.

An extensive collection of exercises is provided, and full solutions are included in an accompanying Student Solutions Manual.