user16859
Reputation
280
Next privilege 500 Rep.
Access review queues
Badges
2 9
Newest
Impact
~12k people reached

• 0 posts edited
• 0 helpful flags
• 20 votes cast

39 Comments

 Jun4 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. Apr30 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. Apr30 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. Apr30 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? Apr22 comment The spectrum of a bounded linear operator Thank you. I basically proved that. Apr22 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 Apr22 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. Apr19 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? Apr15 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! Apr10 comment About the notation of the probability measures I checked the textbook. They are the same. Apr10 comment About the notation of the probability measures Thank you. I saw this argument somewhere. So you think we have $\mu_{n}\overset{w}{\rightarrow}\mu\Leftrightarrow P^{X_{n}}\overset{w}{\rightarrow}P^{X}$ ? Apr10 comment About the notation of the probability measures So do we have "$\mu_{n}\overset{w}{\rightarrow}\mu\Leftrightarrow P^{X_{n}}\overset{w}{\rightarrow}P^{X}$"? Apr9 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. Apr9 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 Apr9 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. Apr9 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. Mar16 comment Matrix norm $T:l_{\infty}^{2}\rightarrow l_{\infty}^{2}$ Thank you! It is very helpful. Mar15 comment Hahn-Banach. Extend the functional by continuity Finally, problem solved. Thank you so much! Mar15 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. Mar15 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.