 Coordinate criterion for weak convergence in a separable Hilbert space (source code)

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= Coordinate criterion for weak convergence in a separable Hilbert space

For a Hilbertian basis $(e_i)$, a sequence $x_n$ converges weakly if and only if $(x_n)$ is norm bounded and every coordinate sequence $\langle x_n,e_i\rangle$ converges.

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