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 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 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.
Sample Chapter(s)
Chapter 1: Basic Elements of Metric Topology (650 KB)
Contents:
- Basic Elements of Metric Topology
- New Types of Function Spaces
- Theory of Hilbert Spaces
- Operators on Hilbert Spaces
- Spectral Theory
- Exercises and Applications
Readership: Undergraduates in mathematical and physical sciences, and electrical and electronic engineering.
