Abstract
A Banach space X is Grothendieck if the weak and the weak* convergence of sequences in the dual space X* coincide. The space l(infinity) is a classical example of a Grothendieck space due to Grothendieck.
We introduce a quantitative version of the Grothendieck property, we prove a quantitative version of the above-mentioned Grothendieck's result and we construct a Grothendieck space which is not quantitatively Grothendieck. We also establish the quantitative Grothendieck property of L-infinity(mu) for a sigma-finite measure mu. (C) 2013 Elsevier Inc.
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