[Math] A book you would like to write

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Writing a book from the beginning to the end is (so I heard) a very hard process. Planning a book is easier. This question is dual in a sense to the question "Books you would like to read (if somebody would just write them)". It is about a book that you feel you would like to write (if you just have the time). A book that will describe a topic not yet properly discribed or give a new angle to a subject that you can contribute.

The question is meant to refer to realistic or semi-realistic projects (related to mathematics). Answers about book projects based on existing survey articles or lecture notes can be especially useful.

Of course, If you had some progress in writing a book mentioned here please please update your answer!

Best Answer

Gosh, what a question, Gil. What is your answer?

I have written many books in my head, but I am much too lazy actually to write a book. I guess my first choice would be

Geometric nonlinear functional analysis, volume II

and my third choice

Geometric nonlinear functional analysis, volume III

neither of which will ever be written by the authors of volume I.

A less daunting topic, until you think about it a lot, is

The geometry of $L_p$ spaces.

Another one I toyed with was

Approximation properties of Banach spaces.