Recent content by prophetlmn

So we have \begin{eqnarray*} \lim_{N\rightarrow +\infty} \frac{1}{\sqrt{N}}\sum_n \|f_n \chi_{[-N,N]}\|_2\\ &\leq & \sum_n\lim_{N\rightarrow +\infty} \frac{1}{\sqrt{N}} \|f_n \chi_{[-N,N]}\|_2\\ \end{eqnarray*} ? if so how to prove it?i.e. how you get the following \begin{eqnarray*}...

so you mean here we should use something like Fatou's lemma?

I still have two little problems (1)what do you mean by 'Thus by monotone convergence',I mean don't you just use the definition of ##\sum_n \|f_n\|## (2)why you use limsub in the last three steps \begin{eqnarray*} \lim_{N\rightarrow +\infty} \frac{1}{\sqrt{N}}\left\| \sum_{n=m}^{+\infty}...

thanks for your help,the proof is very clear,the key point is 'a space is is complete iff every absolute convergent series is convergent',I don't know this before, it's again the old truth 'take a different approach'

also see http://planetmath.org/exampleofnonseparablehilbertspace the main difficulty is about the completeness, which is hard to prove, the author's hint seems don't work here, for you can not use the monotone convergence theorem directly , f(x)χ[-N,N]/sqrt[N] is not monotone

thanks, would you tell me the name of this book? I remember this guy is the author of 2nd edition of J.J Sakurai's Modern quantum mechanics, an experimental physics. Experiments in modern physics, 2nd ed is it this one?

Hi guys,do you have any suggested book on Laboratory physics? I mean something beyond simple freshman experiments such as verify Newton's second law, but still keep general viewpoints, and focus on important experiments in modern physics,for example the S-G experiment of spin magnetic moment...

yes，but i mean another kind of proof，as i know from one of my friend if the metrics are compact then the condtion for A and B is necessary，while in general it‘s not，I have nearly got a proof about this yesterday，but tonight I found there is a small mistake in my proof，and l still have not got a...

Given X=R∞ and its element be squences let d1(x,y)=sup|xi-yi| let d∞(x,y)=Ʃ|xi-yi| then there exists some some x(k) which convergences to x by d1 but not by d∞ ,for example let x be the constant squence 0, i.e xn=0 ,and let x(k)n=(1/k2)/(1+1/k2)n then d1(x(k),x)=1/k2 and...

Given X=R∞ and its element be squences let d1(x,y)=sup|xi-yi| let d∞(x,y)=Ʃ|xi-yi| then there exists some some x(k) which convergences to x by d1 but not by d∞ ,for example let x be the constant squence 0, i.e xn=0 ,and let x(k)n=(1/k2)/(1+1/k2)n then d1(x(k),x)=1/k2 and...

I agree with that as a theoretical physicist you can develop all sorts of skills which are most useful in the industrial world take away from specialization in a theoretical area. and what's more, as a theoretical physicist (of mid level or higher),especially the ones work on fundamental...

i've solved this problem by apply zorn's lemma instead of use AC directly.consider the set of well ordered sets of X,by Halmos' lemma every chain (respect to continuation)in it has an upper bound,so it has an maximal element.this maximal element is cofinal. does anyone knows other methods?for...

How to prove that 'every totally ordered set X contains a cofinal well-ordered subset'? I'm reading Halmos's Navie set theory,this is an excersice in the chapter 'well-ordering'. According to Halmos( in the same chapter),if a set C cotains well-orderd sets,and it is a chain respect to...

my ebook is as the same as these two,no toc no chapter 1. Maybe you are right,it's an unpublished notes,just like some of Georch's lectures.

yes,when I downalded this one,its title said that it's written by Gross.I had google it,but found only F.Gross's book.I'm not sure whether it's written by D.Gross.Do you know any more details about this? Thank you for your help