The concept of weak convergence in Hilbert spaces - Ferreira, M. A. M.; Andrade, M.; Filipe, J. A. (Proceedings of 12th Conference on Applied Mathematics, APLIMAT 2013, 2013)
In order to generalize the Bolzano-Weierstrass Theorem, a weaker notion of convergence is introduced. Then it is discussed in which conditions weak convergence implies convergence. The results presented are in the domain of the real Hilbert spaces.