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seen Oct 19 at 23:23

Oct
19
comment Beautiful cyclic inequality
Bring to the same common denominator, expand, and this should follow from Muirhead Inequality.
Oct
19
comment Beautiful cyclic inequality
I think it should be $a^3$ not $a^2$ in the denominator.
Oct
16
comment Family of sequences in a Hilbert space with certain property
Yes, I think it's all good now. Thanks!
Oct
16
accepted Family of sequences in a Hilbert space with certain property
Oct
16
comment Family of sequences in a Hilbert space with certain property
I mean $$z=\sqrt{2}\sum_i(-1)^{i+1}\frac{1}{(\sqrt{3})^i}e_i$$
Oct
16
comment Family of sequences in a Hilbert space with certain property
I don't think this is a counterexample. I don't ask that $z$ "cancels" all elements of $\mathcal{F}$, but only one. If you take $z=\sqrt{2}\sum_i\frac{1}{(\sqrt{3})^{i}}e_i$, then $\langle z, z_{2,k} \rangle=0$ for any $k$.
Oct
16
comment Family of sequences in a Hilbert space with certain property
I edited the original question, it had a fairly easy counterexample. Now, the question seems less trivial.
Oct
16
revised Family of sequences in a Hilbert space with certain property
deleted 36 characters in body
Oct
16
comment Family of sequences in a Hilbert space with certain property
@daw You are right. Fixed, I require the sequence to be non-zero.
Oct
16
revised Family of sequences in a Hilbert space with certain property
added 9 characters in body
Oct
16
comment Family of sequences in a Hilbert space with certain property
Unit sphere of $l_2$.
Oct
16
asked Family of sequences in a Hilbert space with certain property
Jul
2
awarded  Curious
May
18
comment A problem with concyclic points on $\mathbb{R}^2$
Awesome proof. And since it depends heavily on Sylverster-Gallai it is very unlikely a naive proof as I attempted would work.
May
18
comment A problem with concyclic points on $\mathbb{R}^2$
Maybe I misunderstand, but in Lemma 1, you take $C'$ to be the intersection points between lines $Q_1Q_j$ with $\Pi$, and not the projections of $Q_j's$ onto $\Pi$, right?
May
18
comment A problem with concyclic points on $\mathbb{R}^2$
I posted it as an answer, way too long fr a comment.
May
18
answered A problem with concyclic points on $\mathbb{R}^2$
May
17
accepted Operators with finite spectrum
May
17
comment A problem with concyclic points on $\mathbb{R}^2$
Very interesting problem! I did it for 4,5,6,7,and 9 points, it is a fairly easy counting argument. But other than that....I tried to do it for 8 points, but I could not.
May
15
accepted Density of union of closed sets