Dear Colleagues,
Could you please help me in solving the following problem:
Show that the subspace consisting of all such that is complete.
Best Regards.
Perhaps simpler than pure definition (though not much) is to notice that the linear functional is continuous and thus (our set) is a closed subspace of the complete space and thus complete (this is easier assuming that you know (which I've stated to you before and which is a very simple fact) that the evaluation functionals is continuous and thus continuous).