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Jul 23, 2020 at 20:22 comment added April Thanks for the clarification!
Jul 23, 2020 at 20:19 comment added Piotr Hajlasz @April I only answered the first questions and I do not have an answer for the second one. I would still expect a counterexample, but I do not have a proof. Just a guess.
Jul 23, 2020 at 20:16 comment added April Thanks for providing an example of an ONB for which the desired result does not hold. But it doesn't answer my question which is: can we always choose an ONB where the desired result holds.
Jul 23, 2020 at 20:11 history edited Piotr Hajlasz CC BY-SA 4.0
added 12 characters in body
Jul 23, 2020 at 20:05 history answered Piotr Hajlasz CC BY-SA 4.0