user16859

233 reputation

bio	website
	location
	age
visits	member for	1 year, 7 months
	seen	May 7 '12 at 22:10
stats	profile views	58

	233 reputation	bio	website		visits	member for	1 year, 7 months
16 badges		location			seen	May 7 '12 at 22:10

summary answers questions tags badges favorites bounties reputation activity

39 Comments

suggestions reviews revisions comments badges posts accepts all

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 28	comment	Interior of a balanced set The sufficient condition is a theorem in Rudin.
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.