Functional Analysis: Entering Hilbert Space- 2Nd Ed

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 pth power Lebesgue integral functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of hölder and minkowski. The lp-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. In this second edition, I have expanded the material on Normed vector spaces and their operators presented in br>Chapter 1 to include proofs of the open mapping theorem, the closed graph theorem and the Hahn– Banach theorem.