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Feb
11
comment Conditions for Real and Complex Inner Product Spaces
@Jamil_V What operations define $\langle\cdot,\cdot\rangle_r$ depends on what operations define $\langle\cdot,\cdot\rangle$ since $\langle\cdot,\cdot\rangle_r$ is defined to be the real part of $\langle\cdot,\cdot\rangle$. If $E$ is the space $L^2$ then the definition of $\langle\cdot,\cdot\rangle$ involves an integral. But since you don't have more information about $E$ you cannot say more about $\langle\cdot,\cdot\rangle_r$.
Jan
16
comment If a sequence of points approaches a convex compact set, then the limit of Cesàro means is in the set
What's a realtion?
Jan
16
comment If $f$ is continuous & $\lim_{|x|\to {\infty}}f(x)=0$ then $f$ is uniformly continuous or NOT?
Great answer, just enough detail to be able to write down a proof : )
Jan
16
comment Why is $R-\lambda$ invertible for $|\lambda|<1$
@Marc Did you do it?
Jan
14
comment Why is $R-\lambda$ invertible for $|\lambda|<1$
@Marc Yes I can explain but I think you should try to verify this yourself. I feel that I already gave away too much information. I'll let you try and if you can't figure it out in the next 24 hours I'll add the full calculation.
Dec
28
comment Kreyszig's Functional Analysis Section 2.8: How is the canonical embedding map injective?
Certainly. Hahn Banach does not apply here, I deleted what I had written.
Dec
28
comment Kreyszig's Functional Analysis Section 2.8: How is the canonical embedding map injective?
And btw it's "Kreyszig" not "Kryszeg". Please also correct the spelling of his name in your other questions.
Dec
27
comment What objects can belong in a group?
All characters appearing in this work are fictitious. Any resemblance to real persons, living or dead, is purely coincidental.
Dec
27
comment Does $(X)(Y)=(XY)$ for $X,Y\subseteq R$?
@egreg Can you point me to a definition of "freely generated algebra"? I can only find "finitely generated algebra". Thanks in advance.
Dec
26
comment Does $(X)(Y)=(XY)$ for $X,Y\subseteq R$?
Perhaps you want to replace the tag examples-counterexamples by solution-verification?
Dec
22
comment consider the normed linear spaces $(\mathcal C[0,1], ||.|| _i)$.what can you conclude about the correspoding open unit balls?
math.stackexchange.com/questions/66029/…
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
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?