A note on weak convergence in Hilbert spaces
Manuel Ferreira
Jose Filipe2012
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Abstract
In the Hilbert spaces domain, it is discussed in this work under which conditions weak convergence implies convergence.
Key takeaways
- It is natural after (1) to pose the following question:
- Suppose that converges weakly for x and ‖ ‖ for ‖ ‖.
- Suppose that converges weakly for x.
- -Due to the weak convergence, it is possible to choose , such that , < 1,
- Take a subsequence , and put = , in order that ( ) = lim ( ) and, still, that ∑ converges for x, in accordance with Theorem 1.2.
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