Elementary Banach Space Theory: An Engaging Introduction

This volume is a much needed introduction to Banach Space Theory for the beginner. There are a number of quality books on Banach Space Theory already written. However, they have several disadvantages in common. None of those books is accessible to undergraduates. All are quite expensive, as math textbook frequently are. Most importantly, for the reader who is not already enthralled by Banach Space Theory, these books can be intimidating and possibly even dry. In contrast, this book seamlessly weaves information on Banach Space Theory into a highly entertaining and suspenseful detective story. In addition, readers will find this book satisfying as it gives the definition of a Banach Space and several examples within the first few pages. To understand what a Banach Space is, one must understand the word "complete", "normed", and "vectorspace". The book proceeds to define and explain these additional concepts. Since these concepts depend in turn on additional concepts, the book continues to unpeel layer upon layer of definitions. By immediately learning the definition of a Banach Space and some examples thereof, the reader is motivated to want to understand the concepts that underlie that most fascinating idea. The interwoven detective story, meanwhile, will appeal to modern readers who wish to be entertained on multiple levels.