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Continuous restrictions of linear functionals. (English) Zbl 0808.46020

The authors construct a linear map from \(\ell_ 1\) to \(\mathbb{R}\) which does not have a continuous restriction to any closed infinite-dimensional subspace of \(\ell_ 1\).

MSC:

46B10 Duality and reflexivity in normed linear and Banach spaces
46B45 Banach sequence spaces
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