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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
comment Prove: $\frac1x$ is not a uniformly continuous function
@Bungo Thank you!
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
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.
Nov
28
comment Cancellation of Direct Product in Grp
How do you read $\times$-compact? "product compact"? Did you invent this definition?
Nov
25
comment $\Bbb{R}^2$ not homeomorphic to $\Bbb{R}^2\setminus \{0\}$
Your question was answered here: math.stackexchange.com/a/30888/5798
Nov
24
comment Circle to circle homotopic to the constant map?
Ah, great, I understand. I think I can write the proof. Thank you very much for your comment!
Nov
23
comment Circle to circle homotopic to the constant map?
To get the extension do you apply some generalisation to $\mathbb R^2$ of Tietze's extension theorem?
Nov
18
comment Open and closed complex sets
Or one of the real parts was meant to be imaginary?
Nov
16
comment $\left\{\,f\in L^1[0,1]\,\big\vert\,\int_0^1\lvert f\rvert^2>1\right\}$ is open
Wouldn't it be easier to show that the closed unit ball is sequentially closed?
Nov
16
comment Does a continuous point-wise limit imply uniform convergence?
@IlmariKaronen Thank you for your comment! This is a great answer. I hope it gets some more upvotes.
Nov
16
comment Does a continuous point-wise limit imply uniform convergence?
Do I understand correctly: $f_n$ looks like a triangle getting smaller at the base? (piecewise linear function)
Nov
5
comment Counterexample to the set of all algebraic polynomials being dense in $[0,1]$
I see. So I guess an algebraic polynomial is the same as a polynomial. : )
Nov
5
comment Counterexample to the set of all algebraic polynomials being dense in $[0,1]$
What is an algebraic polynomial?
Oct
29
comment Showing that $f$ continuous
@sammath I added an open set proof.