Compact and Hilbert–Schmidt Operators

Abstract

Although compact operators play an important role in many areas of analysis, they appear only rarely in this volume. In particular, we use them in the proof of Theorem 5.26, and the special type of compact operators known as Hilbert–Schmidt operators play a role in some exercises that deal with tensor products. This appendix provides a brief review of the properties of compact and Hilbert–Schmidt operators that are relevant to our uses in this volume. A few proofs are included, and some others are sketched in the Exercises for this appendix.