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Norbert's user avatar
Norbert's user avatar
Norbert
  • Member for 12 years, 6 months
  • Last seen this week
140 votes
Accepted

Relations between p norms

69 votes
Accepted

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

51 votes
Accepted

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

43 votes

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

37 votes
Accepted

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

31 votes
Accepted

Proving that closed (and open) balls are convex

31 votes

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

31 votes
Accepted

Properties of reflexive Banach spaces

30 votes

Prove that $X'$ is a Banach space

30 votes

Non-closed subspace of a Banach space

29 votes

Gelfand Topology and C*-algebras

28 votes
Accepted

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

28 votes
Accepted

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

28 votes
Accepted

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

23 votes
Accepted

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

23 votes
Accepted

Weak Convergence implies boundedness and componentwise convergence

23 votes
Accepted

The diameter of a compact set.

23 votes
Accepted

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

22 votes

Maclaurin expansion of $\arcsin x$

22 votes
Accepted

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

22 votes
Accepted

Why study operator spaces?

20 votes

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

20 votes

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

19 votes
Accepted

Relationship between cross product and outer product

19 votes

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

19 votes

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

19 votes
Accepted

First theorem in Topological vector spaces.

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
Accepted

Continuity of the adjoint map in various operator topologies

18 votes

Calculating the shortest possible distance between points

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