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Norbert
  • Member for 10 years, 7 months
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117 votes
Accepted

Relations between p norms

63 votes
Accepted

Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$

44 votes
Accepted

How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?

38 votes

$\ell^p\subseteq\ell^q$ for $0<p<q<\infty$ and $\|\cdot\|_q<\|\cdot\|_p$

34 votes
Accepted

Evaluating $ \lim\limits_{n\to\infty} \sum_{k=1}^{n^2} \frac{n}{n^2+k^2} $

31 votes

Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$

28 votes

Prove that $X'$ is a Banach space

28 votes

Gelfand Topology and C*-algebras

27 votes
Accepted

Compute the limit of $\frac1{\sqrt{n}}\left(1^1 \cdot 2^2 \cdot3^3\cdots n^n\right)^{1/n^2}$

26 votes
Accepted

Proving that closed (and open) balls are convex

26 votes
Accepted

Properties of reflexive Banach spaces

25 votes
Accepted

Why is $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ dense in $ L^2(\mathbb{R}^n)$?

24 votes

Non-closed subspace of a Banach space

23 votes
Accepted

Why isometric isomorphic between Banach spaces means we can identify them?

23 votes
Accepted

Inequality. $a^2+b^2+c^2 \geq a+b+c$

22 votes
Accepted

if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant?

22 votes
Accepted

Why study operator spaces?

22 votes
Accepted

Why do we distinguish the continuous spectrum and the residual spectrum?

21 votes
Accepted

Weak Convergence implies boundedness and componentwise convergence

21 votes
Accepted

The diameter of a compact set.

20 votes

Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$

20 votes

Maclaurin expansion of $\arcsin x$

20 votes

Evaluate $\int_{0}^{\infty} \frac{{(1+x)}^{-n}}{\log^2 x+\pi^2} \ dx, \space n\ge1$

19 votes
Accepted

How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?

18 votes

Calculating the shortest possible distance between points

18 votes

Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers

18 votes

How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$?

17 votes
Accepted

First theorem in Topological vector spaces.

16 votes
Accepted

Continuity of the adjoint map in various operator topologies

16 votes
Accepted

Distance between a point and a m-dimensional space in n-dimensional space ($m<n$)

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