Timeline for Mixed up by definitions of mildly mixing
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2016 at 16:20 | comment | added | ARG | thanks for your effort, I was blocked on this direct path, good to know it can follow through. | |
| Mar 14, 2016 at 16:18 | history | edited | ARG | CC BY-SA 3.0 |
gave reference to question 1, added a summary
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| Mar 14, 2016 at 16:15 | comment | added | user78465 | Thanks. I have a direct proof along the lines of what I wrote (by showing the identity $<U_gh,h><|h|^2$ for all simple functions $h$ and approximating). However it is not trivial and Schmidt's proof is clearly more elegant and simpler. | |
| Mar 14, 2016 at 16:05 | comment | added | ARG | thanks, I finally found a proof in "Asymptotic properties of unitary representations and mixing" by K. Schmidt. But his argument is not as direct as yours. | |
| Mar 10, 2016 at 21:16 | comment | added | user78465 | I am not aware of a reference. I will try to write to you my argument in the next few days. | |
| Mar 10, 2016 at 17:03 | comment | added | ARG | hmm... I do get lost in the argument... could you point me to something where this type of argument is done thoroughly? | |
| Mar 10, 2016 at 16:10 | history | edited | ARG | CC BY-SA 3.0 |
corrected the "easy" implication in question 2 (it was the other one...)
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| Mar 10, 2016 at 15:55 | comment | added | user78465 | Your representation is continuous and you can approximate every function by simple functions. | |
| Mar 10, 2016 at 15:52 | comment | added | ARG | Schmidt & Walter also show equivalence of (a) with this other unmentioned definition (product actions being ergodic). I agree (b)=>(a) is easy, because you basically take a characteristic function (+ constant to make it mean zero). But if you have the property on sets, how do you get for any guy in $L^2_0$? This possibly very stupid [sorry for asking], I would just like a reference... The equality you mention is why I wrote "one can reformulate this as ..." | |
| Mar 10, 2016 at 15:33 | comment | added | user78465 | I think that if you look at the paper of Schmidt and Walters you will see also the definition from Glasner's book and its equivalence.Isn't remark 4.28 just something of the form $||\pi(g)h-h||^2=2||h||^2-<\pi(g)h,h>+<h,\pi(g)h>\to 2||h||^2$ as $g$ tends to infinity ? | |
| Mar 10, 2016 at 15:19 | comment | added | ARG | I believe this is a problem of terminology... "no rigid factors" in the paper you quote is defined by (a). The equivalence you cite is with yet another definition of mildly mixing... She "remarks" in 4.28 that what I ask for in Question 1 is "not difficult". I would be very happy to have a reference for this "not difficult" task... and the others... | |
| Mar 10, 2016 at 14:47 | comment | added | user78465 | See section 4 in arxiv.org/pdf/1306.3669v3.pdf (in general this paper is concerned with these questions). She attributes to Schmidt and Walters the proof that (a') iff (a). | |
| Mar 10, 2016 at 10:33 | history | asked | ARG | CC BY-SA 3.0 |