\(H^\infty\) Is a Grothendieck Space.¶
Bourgain, J. (1983). $H^\infty$ Is a Grothendieck Space. Studia Mathematica.
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Domain-specific¶
- Grothendieck Space
- Grothendieck's 1953 work established the property for $C(K)$ when $K$ is compact and Stonean (extremally disconnected), hence for $\ell_\infty=C(\beta\mathbb N)$; these spaces need not be reflexive. Bourgain later proved that the Hardy space $H^\infty$ of bounded analytic functions on the unit disk is Grothendieck.
This sourcePrimary proof for the bounded analytic-function-space example.
- Grothendieck's 1953 work established the property for $C(K)$ when $K$ is compact and Stonean (extremally disconnected), hence for $\ell_\infty=C(\beta\mathbb N)$; these spaces need not be reflexive. Bourgain later proved that the Hardy space $H^\infty$ of bounded analytic functions on the unit disk is Grothendieck.
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