Banach Space Theory: The Basis for Linear and Nonlinear Analysis

When I was learning mathematics, I quickly learned to recognize a kind of book that I (probably unfairly) thought of as a "German-style introduction". Namely, it was called "Introduction to the Theory of X", was 1000 pages long, and included every imaginable result on the theory of X. I found that it was hard to learn a subject from such a book: they were so huge and comprehensive that one lost the thread. On the other hand, such books were incredibly valuable as references, since anything one might want to know could be found within… somewhere.

This book is a German-style introduction to Banach Spaces. The authors have tried to include everything that might be useful in applications in optimization, PDEs, analysis, etc. As a result, most students will find it a bit much. On the other hand, if you need to know what a dentable Banach space is, you can find out here (page 479 has the definition). Most importantly, the book comes with a good set of indices, which should make it a useful reference.

Fernando Q. Gouvêa had never heard of dentable spaces until he looked at this book.