Find the norm of the operator $A: \ell^p \to \ell^p$, $A(x_{n})_{n\geq 1} = (\frac{1}{m}\sum_{n=1}^{m}\frac{x_{n}}{\sqrt{n}})_{m \geq 1}$
38896
Prove that $A$ is bounded operator on $\ell^p$ and find $\| A\|$
51267
Showing a generalized version of the Hölder inequality for $L^{p}$ spaces
87582
Some inequalities between 1- norm, 2- norm and infinity-norm: $\|x\|_2\leq\sqrt{\|x\|_1\| x\|_\infty}\leq\frac{1+\sqrt{n}}{2}\|x\|_2$
62425
Equivalent Definitions of the Operator Norm
132595
$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
33485
norm of integral operator in $C([0,1])$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
17164
How do you show monotonicity of the $\ell^p$ norms?
38761
Is the $ L^{p}$$[0,1]$ norm continuous in p?
46435
2-norm of the orthogonal projection
6278
The value of $\sum_{1\leq l< m <n}^{} \frac{1}{5^l3^m2^n}$
144656
Linear functional and a bounded norm
31302
Hilbert Schmidt Norm-Rank-inequality
81302
Showing that $a_n \in \ell^{\infty}$
81112
Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
70415
Comparison between the $\ell_1$ and $\ell_2$ norms
51302
Show that the operator norm is submultiplicative