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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
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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
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awarded  Teacher
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18
awarded  Notable Question
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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
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Jul
17
revised Distortion and Norm Stabilization
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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
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Jul
17
asked Distortion and Norm Stabilization
Jul
2
awarded  Curious