A non-reflexive Grothendieck space that does not containl ∞
- Richard Haydon
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A compact spaceS is constructed such that, in the dual Banach spaceC(S)*, every weak* convergent sequence is weakly convergent, whileC(S) does not have a subspace isomorphic tol ∞. The construction introduces a weak version of completeness for Boolean algebras, here called the Subsequential Completeness Property. A related construction leads to a counterexample to a conjecture about holomorphic functions on Banach spaces. A compact spaceT is constructed such thatC(T) does not containl ∞ but does have a “bounding” subset that is not relatively compact. The first of the examples was presented at the International Conference on Banach spaces, Kent, Ohio, 1979.
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- A non-reflexive Grothendieck space that does not containl ∞
Israel Journal of Mathematics
Volume 40, Issue 1 , pp 65-73
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- Richard Haydon (1)
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- 1. Brasenose College, Oxford, England