Amudhan
Reputation
1,223
28/100 score
 Mar 24 asked When is the set $\{ x^* x : x \in A\}$ a cone in a *-algebra? Feb 14 comment Trivial norm and topology Every norm induces a metric, not the other way around. The discrete metric does not arise from a norm. Feb 9 accepted Proving $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^3$ Jan 11 awarded Yearling Dec 21 asked Examples of a Banach space with an algebra structure having only left continuity Dec 18 accepted Possible analytic images of the unit disc? Dec 15 comment Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space. I am not looking for a proof of the first statement. I just made it to illustrate how I thought of this question. Dec 15 revised Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space. corrected a wrong assumption Dec 15 revised Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space. added 4 characters in body Dec 15 awarded Informed Dec 15 asked Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space. Dec 15 comment Invertible elements in Banach algebra. hint: try thinking about what $(xy)^{-1}$ should be if $x,y$ are invertible. Dec 14 accepted Want to construct a polynomial with specific properties. Dec 14 comment Want to construct a polynomial with specific properties. Rouche's theorem says that if $|f(z)|<|g(z)|$ on the curve, then $f$ and $f+g$ have the same number of zeros inside the curve. I wanted to know if the theorem holds even if $|f(z)|=|g(z)|$ just for a single point. If I get such a polynomial, then the answer is no. Dec 14 revised Want to construct a polynomial with specific properties. added 1 character in body Dec 14 asked Want to construct a polynomial with specific properties. Dec 14 asked Possible analytic images of the unit disc? Dec 9 accepted Isometric copy of $\ell_1$ in $C[0,1]$? Dec 5 comment Isometric copy of $\ell_1$ in $C[0,1]$? Also, doesn't this proof only work for real $\ell_1$? If I were to extend this map to complex sequences, I think this fails to be an isometry. Is there a way to fix this? Dec 5 comment Isometric copy of $\ell_1$ in $C[0,1]$? I think you meant just $(\alpha_n-1)$, not $(2\alpha_n-1)$.