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Oct 11, 2016 at 22:25 comment added Ben W @BillJohnson Yes I did, and I almost mentioned it above. It was asked in the "Remarks" paper (Kutzarova/Lin, 1998) whether Schlumprecht space $S$ has a unique subsymmetric basis, but to my knowledge that question has never been answered. Nor do I know whether it has ever been investigated to see if $S$ has a symmetric basis (which would give a negative answer to the uniqueness question).
Oct 11, 2016 at 22:13 comment added Bill Johnson Did you check the literature on Schlumprecht's space?
Oct 11, 2016 at 22:08 history edited Ben W CC BY-SA 3.0
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Oct 11, 2016 at 22:00 history asked Ben W CC BY-SA 3.0