Question

Prove this inclusion: $\bigcup_{k<p}\ell^k\subsetneq\ell^p$

score 70 · Answer 1 · 2014-08-07 09:26:55

70

Views

Prove this inclusion: $\bigcup_{k<p}\ell^k\subsetneq\ell^p$

Published on 07 Aug 2014 - 9:26

score 182 · Answer 2 · 2026-04-01 02:02:53

182

Views

Limit of the p-norm of a function on subdomains equals the p-norm of the function on the union domain

Published on 01 Apr 2026 - 2:02

score 55 · Answer 3 · 2014-08-09 23:25:20

55

Views

Maximum value of a mapping on a compact subset of $\ell^{2}$

Published on 09 Aug 2014 - 23:25

score 328 · Answer 4 · 2026-03-31 18:58:54

328

Views

Proof that $(L^1)\neq(L^\infty)^\ast$

Published on 31 Mar 2026 - 18:58

score 161 · Answer 5 · 2014-08-10 13:58:27

161

Views

When does an integral operator belong to the Schatten - von Neumann class in terms of its kernel?

Published on 10 Aug 2014 - 13:58

score 83 · Answer 6 · 2026-04-01 12:55:17

83

Views

Is a $L^1$-function which is linear near the origin in $L^p$?

Published on 01 Apr 2026 - 12:55

score 275 · Answer 7 · 2014-08-14 04:04:21

275

Views

Showing a sequence is in $\ell^2$

Published on 14 Aug 2014 - 4:04

score 85 · Answer 8 · 2026-04-01 02:07:25

85

Views

What does local space of a given Banach space says intuitively?

Published on 01 Apr 2026 - 2:07

score 135 · Answer 9 · 2014-08-15 16:53:37

135

Views

Integrable function with given condition is in $L^p$

Published on 15 Aug 2014 - 16:53

score 92 · Answer 10 · 2014-08-16 14:41:17

92

Views

Dense subset of $L^{2}$ such that $x^{-1/2}f \in L^{1}$ and $\int_{[0, 1]}x^{-1/2}f\, dx = 0$

Published on 16 Aug 2014 - 14:41

score 54 · Answer 11 · 2014-08-18 00:10:41

54

Views

Show that $S = \{f \in L^1(\mathbb{R}) \mid \int_{\mathbb{R}}f dm = 0\}$ is closed in $L^1(\mathbb{R})$.

Published on 18 Aug 2014 - 0:10

score 402 · Answer 12 · 2026-03-30 10:21:24

402

Views

Find the values of $p$ for which the given sequence converges in $l^p$ norm or weakly

Published on 30 Mar 2026 - 10:21

score 105 · Answer 13 · 2026-03-30 10:24:07

105

Views

Weak convergence of scaled elements implies norm convergence

Published on 30 Mar 2026 - 10:24

score 1.3k · Answer 14 · 2026-04-01 02:03:41

1.3k

Views

Is $C^\infty_0$ dense in $C^\infty$ w.r.t. $\|\cdot\|_{L^p}$ and $\|\cdot\|_{W^{1,p}}$?

Published on 01 Apr 2026 - 2:03

score 158 · Answer 15 · 2014-08-22 16:01:21

158

Views

The isomorphism of the Morrey space $L^{2, n} (\Omega)$ and $L^{\infty} \cap L^2 (\Omega)$

Published on 22 Aug 2014 - 16:01

List Question

Prove this inclusion: $\bigcup_{k<p}\ell^k\subsetneq\ell^p$

Limit of the p-norm of a function on subdomains equals the p-norm of the function on the union domain

Maximum value of a mapping on a compact subset of $\ell^{2}$

Proof that $(L^1)\neq(L^\infty)^\ast$

When does an integral operator belong to the Schatten - von Neumann class in terms of its kernel?

Is a $L^1$-function which is linear near the origin in $L^p$?

Showing a sequence is in $\ell^2$

What does local space of a given Banach space says intuitively?

Integrable function with given condition is in $L^p$

Dense subset of $L^{2}$ such that $x^{-1/2}f \in L^{1}$ and $\int_{[0, 1]}x^{-1/2}f\, dx = 0$

Show that $S = \{f \in L^1(\mathbb{R}) \mid \int_{\mathbb{R}}f dm = 0\}$ is closed in $L^1(\mathbb{R})$.

Find the values of $p$ for which the given sequence converges in $l^p$ norm or weakly

Weak convergence of scaled elements implies norm convergence

Is $C^\infty_0$ dense in $C^\infty$ w.r.t. $\|\cdot\|_{L^p}$ and $\|\cdot\|_{W^{1,p}}$?

The isomorphism of the Morrey space $L^{2, n} (\Omega)$ and $L^{\infty} \cap L^2 (\Omega)$

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