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Mar
7
comment Intersection of all neighborhoods of zero is a subgroup
@TobiasKildetoft Thank you for your comment!
Feb
20
comment Are these linear maps bounded?
Seriously: first you pretend you can solve the exercise by "giving" "overgenerous hints" and when I press you for an answer you admit you can't solve it either.
Feb
20
comment Are these linear maps bounded?
I think is clear that the idea of the exercise is to give an explicit example.
Feb
20
comment Are these linear maps bounded?
What's an example of an oscillating function with compact support?
Feb
20
comment Are these linear maps bounded?
Yes, I would like to see an example of a sequence of $f_n$ with $\|f_n\|_\infty \le 1$ and $\|f_n'\|_\infty$ unbounded. Because that's what I've been trying to construct for the past 30 minutes but have not managed. I believe this is what's difficult about this exercise.
Feb
19
comment Are these linear maps bounded?
I also rolled back an entirely unnecessary edit.
Feb
19
comment Are these linear maps bounded?
I upvote in order to compensate for the spite downvote.
Feb
14
comment Hilbert space structure on $C^{*}$ algebras
@JonasMeyer Interesting. Please could you elaborate on your comment?
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 $b^{1/2}$.