The Radon–Riesz property is a concept from functional analysis, particularly in the study of Banach spaces. It concerns the behavior of sequences of functions and their convergence properties. A Banach space \( X \) is said to have the Radon–Riesz property if every sequence of elements \( (x_n) \) in \( X \) that converges weakly to an element \( x \) also converges strongly (or in norm) to \( x \).
Articles by others on the same topic
A normed vector space has the Radon-Riesz property when weak convergence together with implies strong convergence . The Hilbert-space case is the Radon-Riesz theorem. The condition prevents norm from remaining in weakly invisible directions.