Banach spaces

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 (also known as the topology of pointwise convergence) will also converge when is endowed with which is the weak topology induced on by its bidual. 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. (Wikipedia).

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Related pages

Reflexive space | Weak topology | Bounded operator | Banach space | Jean Bourgain | Mathematics | Closure (mathematics) | Separable space | Sequence | Eberlein–Šmulian theorem | Alexander Grothendieck | Hausdorff space | Extremally disconnected space | Open set