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seen Jul 28 at 2:38

Jun
4
comment About inverse matrix in portfolio choice
You are right. I had a typo. In the textbook, there is no 1/2 in Equation (*). Thanks.
Apr
30
comment uniform convergence of continuous functions
I finished all the details but one thing: how can I prove uniform convergence. It seems that even on the compact set, pointwise convergence does not imply uniform convergence. By the way, I would accept the comments as the answer (should you post it or them), since they are very helpful. Thank you.
Apr
30
comment uniform convergence of continuous functions
One quick question: is it right to argue that Convex combination of continuous functions is continuous $\Rightarrow C[0,1]$ is convex.
Apr
30
comment uniform convergence of continuous functions
Riesz representation theorem seems to apply to linear functionals. But C[0,1] meas all continuous functions on [0,1]. Am I wrong?
Apr
22
comment The spectrum of a bounded linear operator
Thank you. I basically proved that.
Apr
22
comment The spectrum of a bounded linear operator
I agree with your ``EDIT''. In fact, $\sigma(T^{n})=[\sigma(T)]^{n}$ for the complex case. That's why the converse is true for the complex. The proof is not trivial. Do you agree? Also @Norbert
Apr
22
comment The spectrum of a bounded linear operator
One simple linear algebra question. Given that $$ T^n-\lambda^nI=\left(\sum\limits_{k=0}^{n-1}\lambda^{n-1-k}T^k\right)(T-\lambda I) $$, why $T^n-\lambda^n I$ is invertible $\Rightarrow T-\lambda I$ is invertible? Thank you.
Apr
19
comment The spectrum of a bounded linear operator
Thank you, but I cannot see how the rotation of matrix is related to this question. Can you clarify a little?
Apr
15
comment About asymmetric simple random walk
I agree with your argument, but that is not the question here. I double checked the question. It is exactly the same as the textbook. But frankly speaking I find this exercise annoying, because later we only need the conclusion that it is bounded. So the upper bound such as yours is sufficient for the later use. Anyway, I can not argue that the exercise is wrong. Thank you!
Apr
10
comment About the notation of the probability measures
I checked the textbook. They are the same.
Apr
10
comment About the notation of the probability measures
Thank you. I saw this argument somewhere. So you think we have $\mu_{n}\overset{w}{\rightarrow}\mu\Leftrightarrow P^{X_{n}}\overset{w}{\rightarrow}P^{X}$ ?
Apr
10
comment About the notation of the probability measures
So do we have "$\mu_{n}\overset{w}{\rightarrow}\mu\Leftrightarrow P^{X_{n}}\overset{w}{\rightarrow}P^{X}$"?
Apr
9
comment Construction of a special continuous function
Yes. It does help. Two answers are basically the same and are provided basically at the same time. The first answer is 1 min earlier. Thank you. I mark this answer as helpful.
Apr
9
comment Construction of a special continuous function
Just one simple question: here the norm means the Euclidean norm. Right? en.wikipedia.org/wiki/Euclidean_norm#Euclidean_norm
Apr
9
comment Construction of a special continuous function
Thank you! I copied the original text. I guess it should mean for all $\epsilon>0$. I don't know how to modify the bump function to make it continuous.
Apr
9
comment Weak convergence of Dirac measures
Thank you, Byron. I edited the question to make it more specific. Could you please further clarify it? Thanks.
Mar
16
comment Matrix norm $T:l_{\infty}^{2}\rightarrow l_{\infty}^{2}$
Thank you! It is very helpful.
Mar
15
comment Hahn-Banach. Extend the functional by continuity
Finally, problem solved. Thank you so much!
Mar
15
comment Hahn-Banach. Extend the functional by continuity
@t.b. I figured out everything except one question: I need to use $x_n\rightarrow x\Rightarrow \lim ||x_n||=||x||$. I guess it should be OK, but I feel I have not seen such a property before.
Mar
15
comment Hahn-Banach. Extend the functional by continuity
@t.b Thanks a lot. I guess that general fact is base on Tietze extension theorem, which I can not use without proof. So I will probably still try azarel's idea.