Foreword

This book contains complete solutions to the more than six hundred exercises

in the authors' book: An Invitation to Operator Theory, American

Mathematical Society, 2002. The problems have been spread over eleven

chapters following the format of that book. Each problem is identified by

a triplet of numbers x.y.z; x designates the chapter, y the section, and z

the exercise. For instance, Problem 3.4.7 indicates Exercise 7 in Section 4

of Chapter 3.

All solutions are based on the material covered in the text with frequent

references to the results in the text. For example, a reference to Theorem 5.9

refers to Theorem 5.9 and a reference to Example 6.21 refers to Example 6.21

in the book An Invitation to Operator Theory. We have added an extra

amount of material to many solutions in order to make this book as self-

contained as possible.

This problem book

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be beneficial to students only if they use it

"properly," that is to say, if students look at a solution of a problem only after

trying very hard to solve the problem. Students will do themselves great

injustice by reading a solution without any prior attempt on the problem.

It should be a real challenge to students to produce solutions which are

different from the ones presented here.

Due to the extra material incorporated into the problems, the book

can be used as a companion supplement to any text used for the standard

functional analysis graduate courses. In addition, this solution book can be

used as a reference not only for mathematical subjects but also for other

disciplines that rely on functional analytic or measure theoretic techniques.

XI