Question

Prove that $\| v \|_{1} \|v\|_\infty \leq \frac{1+\sqrt{n}}{2} \|v\|^{2}_{2}$

score 153 · Answer 1 · 2019-10-28 00:30:41

153

Views

Prove that $\| v \|_{1} \|v\|_\infty \leq \frac{1+\sqrt{n}}{2} \|v\|^{2}_{2}$

Published on 28 Oct 2019 - 0:30

score 190 · Answer 2 · 2019-10-28 02:37:00

190

Views

Smoothness of a Banach Space

Published on 28 Oct 2019 - 2:37

score 64 · Answer 3 · 2019-10-28 04:36:44

64

Views

show that $\lim_{n\to \infty} \|f\|_n=\lim_{n\to \infty} \frac{\|f\|_{n+1}^{n+1}}{\|f\|_{n}^{n}}=\|f\|_\infty$

Published on 28 Oct 2019 - 4:36

score 602 · Answer 4 · 2026-03-27 16:55:09

602

Views

Proof of Interpolation Inequality in $L^p$ Spaces

Published on 27 Mar 2026 - 16:55

score 104 · Answer 5 · 2026-04-03 12:53:50

104

Views

Fourier coefficient $ \hat{f}(n) $ and $\|f\|_1$

Published on 03 Apr 2026 - 12:53

score 135 · Answer 6 · 2019-10-29 05:35:29

135

Views

Show that $g(x) = \int_E f(x − t)d\lambda(t)$ is continuous on $\mathbb{R}$

Published on 29 Oct 2019 - 5:35

score 38 · Answer 7 · 2019-10-29 13:00:25

38

Views

On a normed space if $\|u+v\|=\|u\|+\|v\|$ then $\forall s,t \geqslant 0$ we have that $\|su+tv\|=s\|u\|+t\|v\|$

Published on 29 Oct 2019 - 13:00

score 66 · Answer 8 · 2019-10-29 22:11:35

66

Views

Determine the unique minimum-norm solution to a compatible linear system

Published on 29 Oct 2019 - 22:11

score 63 · Answer 9 · 2019-10-30 04:04:31

63

Views

if $\|f_n\|\leq 1$ then $\|f\|\leq 1$

Published on 30 Oct 2019 - 4:04

score 302 · Answer 10 · 2026-03-28 04:34:29

302

Views

Show that $B_j$ is a Cauchy sequence with respect to the operator norm

Published on 28 Mar 2026 - 4:34

score 63 · Answer 11 · 2019-10-30 18:57:12

63

Views

for each function $g \in L^2(X, \mu)$, $\int fgd\mu=\lim_{n\to \infty}\int f_ngd\mu$

Published on 30 Oct 2019 - 18:57

score 139 · Answer 12 · 2019-10-31 09:42:40

139

Views

Let $\mathcal C^1([0,1],\mathbb R)$ be endowed with the norm $\|\cdot\|$. Prove that $\|f\|_\infty \le\|f\|$

Published on 31 Oct 2019 - 9:42

score 16 · Answer 13 · 2026-03-10 22:42:22

16

Views

Show that $\|(T \circ T(f))' - (T \circ T(g))' \|_{\infty} \le \frac{1}{4}\|f-g\|_{\infty}$

Published on 10 Mar 2026 - 22:42

score 29 · Answer 14 · 2019-10-31 21:27:29

29

Views

Show that $\frac{||L|| \ ||U||}{||A||} < \min(κ(L),κ(U))$, when $A=LU$ andv$ A$, $L$, $U$ both non-singular

Published on 31 Oct 2019 - 21:27

score 53 · Answer 15 · 2019-11-01 15:28:13

53

Views

In 2-norm case, if L is unitary, $\frac{\||L|\|_2\||U|\|_2}{\||A|\|_2} \leq n$

Published on 01 Nov 2019 - 15:28

List Question

Prove that $\| v \|_{1} \|v\|_\infty \leq \frac{1+\sqrt{n}}{2} \|v\|^{2}_{2}$

Smoothness of a Banach Space

show that $\lim_{n\to \infty} \|f\|_n=\lim_{n\to \infty} \frac{\|f\|_{n+1}^{n+1}}{\|f\|_{n}^{n}}=\|f\|_\infty$

Proof of Interpolation Inequality in $L^p$ Spaces

Fourier coefficient $ \hat{f}(n) $ and $\|f\|_1$

Show that $g(x) = \int_E f(x − t)d\lambda(t)$ is continuous on $\mathbb{R}$

On a normed space if $\|u+v\|=\|u\|+\|v\|$ then $\forall s,t \geqslant 0$ we have that $\|su+tv\|=s\|u\|+t\|v\|$

Determine the unique minimum-norm solution to a compatible linear system

if $\|f_n\|\leq 1$ then $\|f\|\leq 1$

Show that $B_j$ is a Cauchy sequence with respect to the operator norm

for each function $g \in L^2(X, \mu)$, $\int fgd\mu=\lim_{n\to \infty}\int f_ngd\mu$

Let $\mathcal C^1([0,1],\mathbb R)$ be endowed with the norm $\|\cdot\|$. Prove that $\|f\|_\infty \le\|f\|$

Show that $\|(T \circ T(f))' - (T \circ T(g))' \|_{\infty} \le \frac{1}{4}\|f-g\|_{\infty}$

Show that $\frac{||L|| \ ||U||}{||A||} < \min(κ(L),κ(U))$, when $A=LU$ andv$ A$, $L$, $U$ both non-singular

In 2-norm case, if L is unitary, $\frac{\||L|\|_2\||U|\|_2}{\||A|\|_2} \leq n$

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