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Answer by user147263 for Sequence of linear functionals
I think the solution suggested by Jochen is the intended one for this exercise. By the closed graph theorem, it suffices to prove that if $x_k\to x$ and $\Phi x_k\to y$, then $\Phi(x)=y$. The equality...
View ArticleSequence of linear functionals
There is the sequence of lienar functionals $\phi_n:X\rightarrow\mathbb{R}$, $n=0,1,\dots$ on the Banach space $X$ for which the map:$$\Phi:X \ni x\rightarrow(\phi_n(x))_{n=0}^{\infty}\in \ell^{1}$$is...
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