Riesz F., Sz.-Nagy B. Functional analysis

The first part covers the modern theories of differentiation and integration and serves as an introduction to the second, which deals with integral equations and the theory of linear operators in Hilbert space. The two parts form an organic unit centred about the concept of the linear operator. This concept is reflected in the method by which the Lebesque integral is constructed.
The section on Hilbert space covers a considerable portion of the known theory including some of the latest results.
The is also a separate chapter on completely continuous operators.