Dear Students,

 

I will be teaching Functional Analysis in Fall 2018 to be continued in

Spring 2019. After an extensive search for a suitable textbook, I have

made my decision. The textbook for the course will be "Functional

Analysis (Methods of Modern Mathematical Physics)" by Michael Reed and

Barry Simon.

 

https://www.amazon.com/Functional-Analysis-Methods-Mathematical-Physics/dp/0125850506

 

 

The following quote is from the Amazon page above

 

This book is the first of a multivolume series devoted to an

exposition of functional analysis methods in modern mathematical

physics. It describes the fundamental principles of functional

analysis and is essentially self-contained...

 

The following quote is from the review by J. A. Goldstein

The American Mathematical Monthly

Vol. 80, No. 10 (Dec., 1973), pp. 1152-1153

 

"The book has many strong features, including

the selection of topics, the notes, the exercises, the applications,

the chapter on

locally convex spaces, etc. Even the students who had no knowledge of

(or interest in)

physics appreciated the fact that the analysis they were studying is

useful outside of

mathematics, and this is an important motivating factor."

 

Quote from a review on Amazon

 

"Books on mathematical methods "for physicists" are often criticized

by their superficiality, a sacrifice deemed necessary for achieving

completeness. This one is a glaring exception: the first of a set of 4

(!) volumes dealing with the finest tools for dealing with the

delicate mathematical questions in quantum theory - namely, functional

analysis. Of course, this sounds rather vague, since quantum physics

makes use of functional-analytic tools as diverse as distributions,

Hilbert, Banach and locally convex spaces, spectral theory, semigroup

theory, operator algebras, etc.

 

However, do not expect ready-brew formulae and cookbook recipes: this

book gets his job done at least as well as Rudin, Yosida and

Riesz-Sz.Nagy, just to mention the classics. Most theorems are

rigorously proved, and although the book becomes more and more biased

towards mathematical physics [...]  this particular volume has

precisely the most useful stuff: metric, Banach, topological, locally

convex, and Hilbert spaces, bounded and unbounded operators. A

supplement extracted from the second volume with the basics of Fourier

transforms makes it self-contained as a monograph.

 

However, the best things, that make this book nearly unbeatable, are

the several wisely chosen examples and counterexamples, the notes at

the end of each chapter and the wonderful - and useful - exercises.

[...]"

 

Sincerely,

 

Jerzy Wojciechowski