THE WEAK CONVERGENCE IN HILBERT SPACES CONCEPT CONSTRUCTION (REVISITED)

Abstract

We intend in this article critically review the weak convergence concept in the real Hilberti spaces domain. Indeed, the purpose is to review, correct and enlarge the paper by Ferreira (2014) on this subject, where is studied mainly its construction process. The main goal is to enlarge the Bolzano -Weierstrass theorem field of validity. Then it is discussed in which conditions weak convergence implies convergence.