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 5h awarded Notable Question Mar19 awarded Popular Question Feb13 awarded Popular Question Oct21 awarded Popular Question Jul18 accepted Distortion and Norm Stabilization Jul18 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 $Y$). Jul17 revised Distortion and Norm Stabilization added 6 characters in body Jul17 revised Distortion and Norm Stabilization added 1 character in body Jul17 comment Distortion and Norm Stabilization @ChristopherA.Wong: We say that $X$ is distortable if it is $\lambda$-distortable for some $\lambda > 1$. Jul17 revised Distortion and Norm Stabilization added 131 characters in body Jul17 asked Distortion and Norm Stabilization Jul2 awarded Curious Jun5 accepted Correlation Sequences and Unitary Operators Jun5 comment Correlation Sequences and Unitary Operators It came up during a lecture on Fourier Analysis, right before proving Wiener Theorem. I guess it was supposed to be "trivial". Jun5 comment Correlation Sequences and Unitary Operators Never mind, I understand it now. Jun4 comment Correlation Sequences and Unitary Operators How do you know that Wiener's Theorem implies $\frac1N\sum_{n=1}^N|c_n|^2\xrightarrow[N\to\infty]{}0$? I mean, it seems that you're assuming that $\mu$ is continuous. Jun4 revised Correlation Sequences and Unitary Operators edited title Jun4 revised Correlation Sequences and Unitary Operators added 1 character in body Jun3 comment Correlation Sequences and Unitary Operators Is really close. However, my question is about convergence in $\mathbb{R}$, not in $H$ (as in the Mean Ergodic Theorem). I still don't see how to approach this problem... Jun3 revised Correlation Sequences and Unitary Operators edited tags