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arXiv · 1309.4684

Quantitative Grothendieck Property

Hana Bendová
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Abstract

A Banach space $X$ is Grothendieck if the weak and the weak$^*$ convergence of sequences in the dual space $X^*$ coincide. The space $\ell^\infty$ 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 $L^\infty(\mu)$ for a $\sigma$-finite measure $\mu$.

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Hana Bendová. 2013-09-18. Quantitative Grothendieck Property. https://arxiv.org/abs/1309.4684

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