Functional Analysis: Entering Hilbert Space Vagn Lundsgaard Hansen This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of p th power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Holder and Minkowski. The L spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers.This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.