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11h
comment Why's Daugavet equation important?
try dig references given in this paper
19h
answered Radon-Nikodým (write the density as a limit)
2d
comment Conway’s Functional Analysis, VIII §3 Exercise 11
Try expand $f_\alpha$ into series and prove inequality for partial sums.
2d
revised Function equation, find the function evaluated at the certain point.
edited tags
Jun
29
answered Functional Analysis (Topological and Isometric Isomorphisms)
Jun
23
comment Relations between p norms
Then the best constant C is 1.
Jun
23
comment Relations between p norms
@AshokVardhan what does "similar" mean? Do you want to prove something like $\Vert x\Vert_p \leq C\Vert x\Vert_q$ for $p>q$ ?
Jun
20
answered Does any continuous map between two Banach spaces over a nonarchimedian field is a closed map?
Jun
11
comment Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$, is it $\frac{2}{\pi n}$?
Summands $a_i$ attain their maximum at $i=n/4$. So the numerator can be estimated from above as $a_{n/4}\times \frac{n}{2}$. The lower bound is obviously $a_{n/4}$
Jun
10
comment Relations between p norms
@Arun, because for $x=(1,1,1,\ldots,1)$ this bound is attained
Jun
10
comment Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
@AlexM. Thank you!
Jun
10
revised Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
deleted 37 characters in body
May
28
awarded  Necromancer
May
24
comment Showing $r\in\mathbb Q\setminus \{0\}\implies e^r\notin \mathbb Q$
This is a standard trick it is used to prove irrationality of $\pi$, $\tan r$, $e^r$. One just needs to find a suitable integral. I learned that trick from this book
May
23
answered Showing $r\in\mathbb Q\setminus \{0\}\implies e^r\notin \mathbb Q$
May
22
comment Is $B_{\ell_1}$ weak-metrizable?
Correct. $\phantom{}$
May
22
comment Is $B_{\ell_1}$ weak-metrizable?
$\ell_1^*=\ell_\infty$ but $\ell_\infty$ is not separable
May
17
comment What algebraic structure do self-adjoint operators form?
It is a closed cone. Google positive cone of a C*-algebra
May
12
comment Convergence on Norm vector space.
Functional analysis is the study of linear spaces with additional structure
May
1
revised Show: Real roots of a polynomial
edited tags