An unconditional result about Grothendieck spaces

Haydon, Richard

doi:10.1090/S0002-9939-1987-0891155-7

An unconditional result about Grothendieck spaces
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Proc. Amer. Math. Soc. 100 (1987), 511-516 Request permission

Abstract:

It is shown that if $X$ is a nonreflexive Banach spach such that every weak* convergent sequence in ${X^ * }$ is also weakly convergent, then ${X^ * }$ has a subspace isometric to ${L_1}({\left \{ {0,1} \right \}^{{\omega _1}}})$

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