Question

Unsure how $(\ell^1)^*\cong\ell^\infty$

score 212 · Answer 1 · 2026-04-11 23:53:46

212

Views

Unsure how $(\ell^1)^*\cong\ell^\infty$

Published on 11 Apr 2026 - 23:53

score 541 · Answer 2 · 2026-04-13 16:37:40

541

Views

Does Pointwise Convergence imply L2 Convergence in L2?

Published on 13 Apr 2026 - 16:37

score 46 · Answer 3 · 2026-04-16 08:56:12

46

Views

Deciding if $l^1(\mathbb{Z}_+)$ over $\mathbb{F}$ is complete with the norm $\lVert x\rVert=2\left|\sum_{n\geq 1}x_n\right|+\sum_{n\geq2}(1+1/n)|x_n|$

Published on 16 Apr 2026 - 8:56

score 108 · Answer 4 · 2026-04-11 14:15:20

108

Views

Convergence in two $L^p$ spaces

Published on 11 Apr 2026 - 14:15

score 145 · Answer 5 · 2026-04-16 22:28:43

145

Views

Let $\{\phi_n\}$ be an orthonormal set in $L^2(\mu)$, $g\in L^2(\mu)$ such that $|\phi_n(x)|\le |g(x)|$ and $\sum a_n\phi_n(x)$ converges a.e.

Published on 16 Apr 2026 - 22:28

score 50 · Answer 6 · 2026-04-15 19:37:36

50

Views

How to show that the set $S$ is closed in $(c_{0},\|\cdot\|_{\infty})$

Published on 15 Apr 2026 - 19:37

score 18 · Answer 7 · 2026-04-15 22:11:57

18

Views

Showing that $S_k:L^p(X)\to L^p(X), S_kf(x)\equiv f(x + 1/k)$ converges strongly to $I$ but not in norm

Published on 15 Apr 2026 - 22:11

score 84 · Answer 8 · 2026-05-15 14:09:59

84

Views

Sobolev space $H^1(\Omega)$ vs homogeneous Sobolev/Beppo-Levi space $\dot{H}^1(\Omega)$

Published on 15 May 2026 - 14:09

score 83 · Answer 9 · 2026-05-15 14:10:24

83

Views

A property for functions that belong to the fractional Sobolev space $W^{s,p}\left(\mathbb{R}\right)$

Published on 15 May 2026 - 14:10

score 85 · Answer 10 · 2026-04-16 08:45:46

85

Views

Weak closure of the unit sphere in $\ell^p$ is the unit ball?

Published on 16 Apr 2026 - 8:45

score 60 · Answer 11 · 2026-04-17 10:18:09

60

Views

Different answers for adjoint of $T : \ell^2 \to \ell^2$ such that $T(x_1, x_2, \dots) = (c_1 x_1, c_2 x_2, \dots),$ where's the mistake?

Published on 17 Apr 2026 - 10:18

score 114 · Answer 12 · 2026-04-14 16:09:27

114

Views

Inequality in the proof of the atomic decomposition for $L^p$ functions

Published on 14 Apr 2026 - 16:09

score 57 · Answer 13 · 2026-04-15 23:46:38

57

Views

Let $f \in L^1[0,1]$. Does it hold that $\lim_{t\to\infty}t\cdot|\{x:|f(x)|>t\}|=0$?

Published on 15 Apr 2026 - 23:46

score 160 · Answer 14 · 2026-04-15 09:36:01

160

Views

$L^p$ space inequality

Published on 15 Apr 2026 - 9:36

score 50 · Answer 15 · 2026-04-14 02:49:36

50

Views

Hardy's Integral Inequality for $\alpha > -1$ for nonnegative functions with $p \in [1,\infty)$

Published on 14 Apr 2026 - 2:49

List Question

Unsure how $(\ell^1)^*\cong\ell^\infty$

Does Pointwise Convergence imply L2 Convergence in L2?

Deciding if $l^1(\mathbb{Z}_+)$ over $\mathbb{F}$ is complete with the norm $\lVert x\rVert=2\left|\sum_{n\geq 1}x_n\right|+\sum_{n\geq2}(1+1/n)|x_n|$

Convergence in two $L^p$ spaces

Let $\{\phi_n\}$ be an orthonormal set in $L^2(\mu)$, $g\in L^2(\mu)$ such that $|\phi_n(x)|\le |g(x)|$ and $\sum a_n\phi_n(x)$ converges a.e.

How to show that the set $S$ is closed in $(c_{0},\|\cdot\|_{\infty})$

Showing that $S_k:L^p(X)\to L^p(X), S_kf(x)\equiv f(x + 1/k)$ converges strongly to $I$ but not in norm

Sobolev space $H^1(\Omega)$ vs homogeneous Sobolev/Beppo-Levi space $\dot{H}^1(\Omega)$

A property for functions that belong to the fractional Sobolev space $W^{s,p}\left(\mathbb{R}\right)$

Weak closure of the unit sphere in $\ell^p$ is the unit ball?

Different answers for adjoint of $T : \ell^2 \to \ell^2$ such that $T(x_1, x_2, \dots) = (c_1 x_1, c_2 x_2, \dots),$ where's the mistake?

Inequality in the proof of the atomic decomposition for $L^p$ functions

Let $f \in L^1[0,1]$. Does it hold that $\lim_{t\to\infty}t\cdot|\{x:|f(x)|>t\}|=0$?

$L^p$ space inequality

Hardy's Integral Inequality for $\alpha > -1$ for nonnegative functions with $p \in [1,\infty)$

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