Metric functionals and weak convergence
Abstract
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Advanced Banach Space Theory
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Zeitschrift für Analysis und ihre Anwendungen
- Publication date
- 3 June 2026
- Language
- EN