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11h
awarded  Nice Answer
2d
revised group operations are smooth in $\text{SL}(n, \mathbb{R})$
added 273 characters in body
2d
answered group operations are smooth in $\text{SL}(n, \mathbb{R})$
Dec
16
comment If $I$ is a closed ideal in a C*-algebra $A$ and $J$ is a closed ideal in $I$ then $J$ is an ideal of $A$
How does $ab \in J$ follow from $ab^{1/2}\in I$? We have $b \in J^+$ but as far as I can tell there is no reason why we should also have $b^{1/2}$.
Dec
16
comment A concave positive function on $[1,\infty)$ is uniformly continuous
@user161825 It's a pity that there is no badge for it.
Dec
16
comment If $I$ is a closed ideal in a C*-algebra $A$ and $J$ is a closed ideal in $I$ then $J$ is an ideal of $A$
I don't understand your proof. Yes, for all $b \in J^+$ we also have $b \in I$ and therefore $ab,ba \in I$. But it doesn't follow that $ab^{1/2}$ or $ab$ are in $J$.
Dec
16
revised Prove: $\frac1x$ is not a uniformly continuous function
deleted 4 characters in body
Dec
16
comment Prove: $\frac1x$ is not a uniformly continuous function
@Bungo Thank you!
Dec
16
answered Prove: $\frac1x$ is not a uniformly continuous function
Dec
9
awarded  Popular Question
Dec
9
revised Minkowski type inequality in Banach algebras
It's likely to be a Cauchy-Schwarz type inequality since Cauchy died in 1857 and Schwartz was born in 1915.
Dec
9
comment Minkowski type inequality in Banach algebras
Thanks. Now what about changing Cauchy-Schwartz to Cauchy-Schwarz?
Dec
9
comment Minkowski type inequality in Banach algebras
Yeah, just figured it out this very second. Duh. 6 minutes too late.
Dec
9
comment Minkowski type inequality in Banach algebras
Thank you for your comment, I understand. I have one question though: How do you get $AB^\ast = B^\ast A$ and $A^\ast B = B A^\ast$ from $A,B$ normal and commuting?
Dec
7
awarded  Popular Question
Dec
7
comment Minkowski type inequality in Banach algebras
Did you mean for $A+B$ normal? I assume you want to apply the Gelfand representation. In any case, I was wondering if I may change Cauchy-Schwartz to Cauchy-Schwarz.
Dec
6
comment Cardinality of set difference
@Victor Ok, can you post the solution in an answer of your own then? By now you probably know the answer and I'd be interested to see it too.
Dec
6
revised homeomorphism between $2^{\mathbb{N}}$ and the Cantor Middle third set
Unsolicited tag nuked.
Dec
6
answered Reals constructed from equivalence classes of Cauchy sequences of rationals.
Nov
30
answered Cardinality of set difference