Abstract
A Banach space is said to be Grothendieck if weak and weak⁎ convergent sequences in the dual space coincide. This notion has been quantified by H. Bendová. She has proved that ℓ∞ has the quantitative Grothendieck property, namely, it is 1-Grothendieck. Our aim is to show that Banach spaces from a certain wider class are 1-Grothendieck, precisely, C(K) is 1-Grothendieck provided K is a totally disconnected compact space such that its algebra of clopen subsets has the so called Subsequential completeness property.
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