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 Mar 16 comment Classification of subsymmetric basic sequences There is an $u_k$ in you first inequality that should be an $x_k$. I cannot edit it. Mar 16 revised Classification of subsymmetric basic sequences deleted 2 characters in body Mar 16 accepted Classification of subsymmetric basic sequences Mar 16 comment Classification of subsymmetric basic sequences More than clear, Tomek. I would just like to point out that all your argument is possible given that every subsymmetric sequence is seminormalized, that is, there is $C \in [1,\infty)$ such that $\frac{1}{C} \leq \| x_n \| \leq C$ for every $n \in \mathbb{Z}^+$. Mar 16 comment Classification of subsymmetric basic sequences I didn't realize how to use unconditionality. By the way, the inequality involving the unconditionality constant should be reversed, right? Could you elaborate a little more about how you get it? I know that $\left\|\sum_{k=1}^N a_k x_k \right\| \leq K \left\|\sum_{k=1}^N b_k x_k \right\|$ whenever $|a_k| \leq |b_k|$, but I don't see how you used this to arrive to your conclusion. Mar 16 asked Classification of subsymmetric basic sequences Sep 26 awarded Popular Question Jun 5 awarded Teacher Apr 18 awarded Notable Question Mar 19 awarded Popular Question Feb 13 awarded Popular Question Oct 21 awarded Popular Question Jul 18 accepted Distortion and Norm Stabilization Jul 18 comment Distortion and Norm Stabilization Nice answer! The "trick" I did not see was your first inequality; everything follows from it. I think that it is important to note that when you prove that the existence of a distortable subspace $Y$ gives you a non-stabilizing equivalent norm $\lvert \cdot \rvert$, we are implicity using the fact that we can extend $\lvert \cdot \rvert$ from $Y$ to an equivalent norm on $X$ (since, by definition, we need this norm to be defined on the whole space, not just on $Y$). Jul 17 revised Distortion and Norm Stabilization added 6 characters in body Jul 17 revised Distortion and Norm Stabilization added 1 character in body Jul 17 comment Distortion and Norm Stabilization @ChristopherA.Wong: We say that $X$ is distortable if it is $\lambda$-distortable for some $\lambda > 1$. Jul 17 revised Distortion and Norm Stabilization added 131 characters in body Jul 17 asked Distortion and Norm Stabilization Jul 2 awarded Curious