8h
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 $\left|a\right|<1$
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May
31
comment How do I make the conceptual transition from multivariable calculus to differential forms?
@StevenGubkin I was waiting for this explanation for years!
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
Apr
28
revised Can $ {L^{1}}(G) $ be a $ C^{*} $-algebra?
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Apr
27
answered Can $ {L^{1}}(G) $ be a $ C^{*} $-algebra?
Apr
22
answered What is the norm of the pre-multiplication by a fixed matrix operator?
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