Some Notes on Weak Convergence in Hilbert Spaces

EasyChair Preprint 8883

Abstract

We intend in this article critically review the weak convergence concept in the real Hilbert 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.

Keyphrases: Bolzano-Weierstrass Theorem, Hilbert spaces, weak convergence

@booklet{EasyChair:8883,
  author    = {Manuel Alberto M. Ferreira},
  title     = {Some Notes on Weak Convergence in Hilbert Spaces},
  howpublished = {EasyChair Preprint 8883},
  year      = {EasyChair, 2022}}