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The Tirilman spaces $Ti(p,\gamma)$, $1<p<\infty$, were introduced by Casazzaand Shura as variations of the spaces constructed by Tzafriri. We prove thatall subsymmetric basic sequences in the dual space $Ti^*(p,\gamma)$ areequivalent to its canonical subsymmetic but not symmetric basis.

Duals of Tirilman spaces have unique subsymmetric basic sequences