2015/11/06 by Jindřich Lechner, Lechner, Jindřich
Mathematics · Computer Science · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1511.02202
A Banach space is said to be Grothendieck if weak and weak^* convergent sequences in the dual space coincide. This notion has been quantificated 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.