I know there exists an example in the literature due to Per Enflo of a separable Banach space without a Schauder basis. I am wondering if there is a reflexive counterexample?
If so I would greatly appreciate a reference.
2026-03-26 01:01:43.1774486903
Do reflexive separable Banach spaces have Schauder bases?
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An example of a separable reflexive Banach space with no Schauder basis appears in:
Szarek, Stanislaw J., A Banach space without a basis which has the bounded approximation property, Acta Math. 159, 81-98 (1987). ZBL0637.46013.
(I haven't read the paper beyond the statement of the theorem.)