Texts and Readings in Mathematics

This book grew out of a course that the author gave at the Institute of Mathematical Sciences, Chennai. The goal of this book is to begin with the basics of normed linear spaces, quickly specialise to Hilbert spaces and to get to the spectral theorem for bounded as well as unbounded operators on separable Hilbert space.

The first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces The third chapter begins with the standard Gelfand theory of commutative Banch algebras, and proceeds to the Gelfand-Naimark theorem on commutative C* -algebras, followed by a discussion of representations of C* -algebras; the final section of this chapter is devoted to the Hahn-Hellinger classification of separable representations of a commutative C* -algebra. The fourth chapter is devoted to more standard operator theory in Hilbert space. The fifth and final chapter is a brief introduction to the theory of unbounded operators on Hilbert space.