Functional Analysis in Asymmetric Normed Spaces

• Main Author: Cobzaş, Ştefan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Approximation theory.; Functional analysis.; Operator theory.; Topology.; Functional Analysis.; Approximations and Expansions.; Operator Theory.

An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when res...

Table of Contents:

• Introduction.- 1. Quasi-metric and Quasi-uniform Spaces. 1.1. Topological properties of quasi-metric and quasi-uniform spaces
• 1.2. Completeness and compactness in quasi-metric and quasi-uniform spaces.- 2. Asymmetric Functional Analysis
• 2.1. Continuous linear operators between asymmetric normed spaces
• 2.2. Hahn-Banach type theorems and the separation of convex sets
• 2.3. The fundamental principles
• 2.4. Weak topologies
• 2.5. Applications to best approximation
• 2.6. Spaces of semi-Lipschitz functions
• Bibliography
• Index.