ABSTRACT
This chapter is devoted to functions of compact operators, and provides some basic notions of the theory of compact operators. It aims to derive an estimation for the norm of the powers of a Volterra Hilbert-Schmidt operator. The chapter is concerned with an estimation for the norm of the resolvent of a Hilbert-Schmidt operator. It analyzes operators whose powers are Hilbert-Schmidt operators, and also provides estimations for the norm of the resolvent. The chapter investigates compact operators belonging to a NeumannSchatten ideal. The multiplicative structure of the resolvent of a compact operator is treated. By the multiplicative representation of the resolvent, a relation between the determinant and the norm of the resolvent is established for a Hilbert-Schmidt operator with a finite trace.
