Grothendieck space

In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space

in which every sequence in its continuous dual space

that converges in the weak-* topology

which is the weak topology induced on

Said differently, a Grothendieck space is a Banach space for which a sequence in its dual space converges weak-* if and only if it converges weakly.

Then the following conditions are equivalent: This mathematical analysis–related article is a stub.