Metrics, Norms, Inner Products, and Operator Theory

This text is a self-contained introduction to the three main families that we encounter in analysis –  metric spaces, normed spaces , and  inner product spaces  – and to the operators that transform objects in one into objects in another.  With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely present