Grothendieck space

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Grothendieck space, named for Alexander Grothendieck, is a Banach space X such that for all separable Banach spaces Y, every bounded linear operator from X to Y is weakly compact, that is, the image of a bounded subset of X is a weakly compact subset of Y.

Any reflexive Banach space is Grothendieck. Grothendieck spaces which are not reflexive include the space C(K) of all continuous functions on a compact metric space K and the space $L^\infty(\mu)$ for a positive measure $μ$ .