On Weak Convergence and Metrization Issues in Separable Hilbert Spaces
DOI:
https://doi.org/10.65204/djes.v3i3.796Keywords:
Weak convergence; weak topologyAbstract
Background:
Weak convergence is a fundamental concept in infinite-dimensional analysis because it provides a compactness framework when norm convergence is unavailable. In separable Hilbert spaces, a basic dichotomy appears: the weak topology is not metrizable on the whole infinite-dimensional space, while it becomes metrizable on bounded subsets. This distinction plays an important role in functional analysis and variational methods.
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