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Inhaltsverzeichnis

Frontmatter

Chapter 1. Normed spaces

We begin with the fundamental notion of a vector space.
V. S. Sunder

Chapter 2. Hilbert spaces

While normed spaces permit us to study ‘geometry of vector spaces’, we are constrained to discussing those aspects which depend only upon the notion of ‘distance between two points’. If we wish to discuss notions that depend upon the angles between two lines, we need something more — and that something more is the notion of an inner product.
V. S. Sunder

Chapter 3. C*-algebras

The aim of this chapter is to build up the necessary background from the theory of C*-algebras to be able to prove the spectral theorem. We begin with the definition and some examples of a normed algebra.
V. S. Sunder

Chapter 4. Some Operator theory

This section is devoted to specialising several results of the preceding chapter to the case of a ‘singly generated’ commutative C*-algebra, or equivalently to the case of C(∑) where ∑ is a compact subset of the complex plane, or equivalently, to facts concerning a single normal operator on a separable Hilbert space.
V. S. Sunder

Chapter 5. Unbounded operators

This chapter will be concerned with some of the basic facts concerning unbounded operators on Hilbert spaces. We begin with some definitions. It will be necessary for us to consider operators which are not defined everywhere in a Hilbert space, but only on some linear subspace which is typically not closed; in fact, our primary interest will be in operators which are defined on a dense proper subspace. (Since we shall only consider Hilbert spaces, we adopt the following conventions throughout this chapter.)
V. S. Sunder

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