This chapter concerns another important set of compact operators, namely the Hilbert-Schmidt operators. The class of Hilbert-Schmidt operators has a natural Hilbert space structure and it contains the trace class operators. In the first section some additional properties of s-numbers are derived. In the second section the Hilbert-Schmidt operators are introduced and their main properties are established. The last section contains a completeness theorem for eigenvectors and generalized eigenvectors of Hilbert-Schmidt operators.
Unable to display preview. Download preview PDF.