Appendix C: Facts from Hilbert Space Theory

A Hilbert space is a vector space with an inner product \((\mathbf H,\langle \,\cdot \,,\,\cdot \,\rangle )\) which is complete with respect to the metric induced by the inner product. In other words, every Cauchy sequence has a limit in \(\mathbf H\) . To establish notation, we shall give examples of Hilbert spaces which are used in this book.