Grothendieck space

In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space X in which every weakly* convergent sequence in the dual space X* converges with respect to the weak topology of X*. In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space X in which every weakly* convergent sequence in the dual space X* converges with respect to the weak topology of X*. Let X be a Banach space. Then the following conditions are equivalent: