Question

How to find the norm of $ \Lambda x = \sum_{n=1}^{\infty} \frac{x_n}{n\sqrt{6}}$ in $\ell^2$

score 185 · Answer 1 · 2015-01-30 16:42:58

185

Views

How to find the norm of $ \Lambda x = \sum_{n=1}^{\infty} \frac{x_n}{n\sqrt{6}}$ in $\ell^2$

Published on 30 Jan 2015 - 16:42

score 44 · Answer 2 · 2015-02-01 01:29:54

44

Views

Continuity of the multiplication map $f\mapsto x^2 f(x)$ between normed spaces

Published on 01 Feb 2015 - 1:29

score 173 · Answer 3 · 2015-02-03 13:32:54

173

Views

If $(a_n)$ is such that $\sum_{n=1}^\infty a_nb_n$ converges for every $b\in\ell_2$, then $a\in\ell_2$

Published on 03 Feb 2015 - 13:32

score 414 · Answer 4 · 2026-03-26 11:05:06

414

Views

Is $L^2(0,\infty;L^2(\Omega)) = L^2((0,\infty)\times \Omega)$?

Published on 26 Mar 2026 - 11:05

score 808 · Answer 5 · 2026-04-10 23:09:19

808

Views

Adjoint operator of $L^\infty$

Published on 10 Apr 2026 - 23:09

score 367 · Answer 6 · 2015-02-05 00:09:18

367

Views

$μ$ is $σ$-finite iff $L^p(X)$ contains a strictly positive function.

Published on 05 Feb 2015 - 0:09

score 93 · Answer 7 · 2015-02-05 05:53:12

93

Views

Showing some Function $fg$ is Integrable when $g(x)\le e^{-\vert x\vert }$ and given some Conditions on $f$.

Published on 05 Feb 2015 - 5:53

score 81 · Answer 8 · 2015-02-05 16:58:41

81

Views

Discuss the duality relation between $L^p(X)$ and $L^q(X), 1/p + 1/q = 1, $ for $1 ≤ p < ∞.$

Published on 05 Feb 2015 - 16:58

score 337 · Answer 9 · 2015-02-07 03:49:40

337

Views

If $f\in L^1(\mathbb{R})$, then $\sum_{n\ge 1}f(x+n)$ Converges for a.e. $x$.

Published on 07 Feb 2015 - 3:49

score 157 · Answer 10 · 2026-04-12 21:10:17

157

Views

Analogue of Borel-Cantelli Lemma in $L^1(\mathbb{R})$

Published on 12 Apr 2026 - 21:10

score 352 · Answer 11 · 2026-04-13 02:46:46

352

Views

lp and c0 little question

Published on 13 Apr 2026 - 2:46

score 202 · Answer 12 · 2026-03-27 07:49:38

202

Views

Question about this problem If $u \in H^1(U)$, then $Du=0$ a.e. on the set $\{u=0\}$

Published on 27 Mar 2026 - 7:49

score 246 · Answer 13 · 2015-02-09 11:21:10

246

Views

Approximating the gradient of a function by $L^2$ functions (cut-offs)

Published on 09 Feb 2015 - 11:21

score 113 · Answer 14 · 2026-03-29 07:39:24

113

Views

$f\in L^1(\mathbb{R}^N)$ and Lipschitz continuous, then $f\in L^\infty(\mathbb{R}^N)$.

Published on 29 Mar 2026 - 7:39

score 37 · Answer 15 · 2015-02-11 13:37:27

37

Views

Does $\int 1_{|m|>A} m^2$ converge to zero for an $L^2$ function?

Published on 11 Feb 2015 - 13:37

List Question

How to find the norm of $ \Lambda x = \sum_{n=1}^{\infty} \frac{x_n}{n\sqrt{6}}$ in $\ell^2$

Continuity of the multiplication map $f\mapsto x^2 f(x)$ between normed spaces

If $(a_n)$ is such that $\sum_{n=1}^\infty a_nb_n$ converges for every $b\in\ell_2$, then $a\in\ell_2$

Is $L^2(0,\infty;L^2(\Omega)) = L^2((0,\infty)\times \Omega)$?

Adjoint operator of $L^\infty$

$μ$ is $σ$-finite iff $L^p(X)$ contains a strictly positive function.

Showing some Function $fg$ is Integrable when $g(x)\le e^{-\vert x\vert }$ and given some Conditions on $f$.

Discuss the duality relation between $L^p(X)$ and $L^q(X), 1/p + 1/q = 1, $ for $1 ≤ p < ∞.$

If $f\in L^1(\mathbb{R})$, then $\sum_{n\ge 1}f(x+n)$ Converges for a.e. $x$.

Analogue of Borel-Cantelli Lemma in $L^1(\mathbb{R})$

lp and c0 little question

Question about this problem If $u \in H^1(U)$, then $Du=0$ a.e. on the set $\{u=0\}$

Approximating the gradient of a function by $L^2$ functions (cut-offs)

$f\in L^1(\mathbb{R}^N)$ and Lipschitz continuous, then $f\in L^\infty(\mathbb{R}^N)$.

Does $\int 1_{|m|>A} m^2$ converge to zero for an $L^2$ function?

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