Question

Counterexample to show the set$ \left\{(x_{n})\in l^{p}:{\sum_{n=1}^{\infty}}x_{n}=0\right\}$ is not closed in $l^{p}$

score 90 · Answer 1 · 2026-05-03 12:01:45

90

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Counterexample to show the set$ \left\{(x_{n})\in l^{p}:{\sum_{n=1}^{\infty}}x_{n}=0\right\}$ is not closed in $l^{p}$

Published on 03 May 2026 - 12:01

score 329 · Answer 2 · 2026-04-14 03:13:43

329

Views

Linear map on $L^{2}$

Published on 14 Apr 2026 - 3:13

score 198 · Answer 3 · 2026-04-14 16:00:25

198

Views

How to fix this argument that the periodic functions on $[-L/2,L/2]$ generate a dense subspace of $L^2[-L/2,L/2]$?

Published on 14 Apr 2026 - 16:00

score 89 · Answer 4 · 2026-04-16 08:15:21

89

Views

On a finite measure space, can we bound $\lVert f\rVert_1$ given $\lVert f\rVert_2$?

Published on 16 Apr 2026 - 8:15

score 43 · Answer 5 · 2026-04-17 10:57:54

43

Views

Integral of an L_p function

Published on 17 Apr 2026 - 10:57

score 235 · Answer 6 · 2026-04-23 19:32:37

235

Views

Is the $p$-norm of the fourier transform of a function greatest when its phase is constant?

Published on 23 Apr 2026 - 19:32

score 50 · Answer 7 · 2026-04-23 19:26:59

50

Views

Effects of Setting a Lower Bound on the Fourier Transform of a Function

Published on 23 Apr 2026 - 19:26

score 65 · Answer 8 · 2026-04-15 07:19:47

65

Views

Norm of multiplication operator on $L^2[0,1]$ can be achieved

Published on 15 Apr 2026 - 7:19

score 54 · Answer 9 · 2026-04-15 12:38:10

54

Views

Prove that $\{z_n \}_{n \in \Bbb Z} \in \ell^p(\Bbb Z),$ for $p \in [1,\infty).$

Published on 15 Apr 2026 - 12:38

score 212 · Answer 10 · 2026-03-25 23:58:45

212

Views

Show that there exists $M \gt 0$ such that for all $f \in S,$ $\|f\|_{\infty} \leq M \|f\|_2.$

Published on 25 Mar 2026 - 23:58

score 53 · Answer 11 · 2026-04-11 23:24:18

53

Views

$L^4$-norm of a random variable. Why is it computed like that?

Published on 11 Apr 2026 - 23:24

score 167 · Answer 12 · 2026-04-10 04:28:46

167

Views

Volterra integral operator with operator-valued kernel

Published on 10 Apr 2026 - 4:28

score 69 · Answer 13 · 2026-04-15 20:07:11

69

Views

$f\in L^\infty(\mathbb{R}^d)$ has uniform element iff $\Vert\tau_h f-f\Vert_\infty\to0$

Published on 15 Apr 2026 - 20:07

score 78 · Answer 14 · 2026-04-16 20:37:52

78

Views

Lower semi-continuity of the convolution of two nonnegative functions

Published on 16 Apr 2026 - 20:37

score 153 · Answer 15 · 2026-04-17 08:41:03

If $X\subset L^1$ is a closed vector space and $X\subset \bigcup_{1<p\leq\infty} L^p$ then $X\subset L^q$ for some $q>1$.

List Question

Counterexample to show the set$ \left\{(x_{n})\in l^{p}:{\sum_{n=1}^{\infty}}x_{n}=0\right\}$ is not closed in $l^{p}$

Linear map on $L^{2}$

How to fix this argument that the periodic functions on $[-L/2,L/2]$ generate a dense subspace of $L^2[-L/2,L/2]$?

On a finite measure space, can we bound $\lVert f\rVert_1$ given $\lVert f\rVert_2$?

Integral of an L_p function

Is the $p$-norm of the fourier transform of a function greatest when its phase is constant?

Effects of Setting a Lower Bound on the Fourier Transform of a Function

Norm of multiplication operator on $L^2[0,1]$ can be achieved

Prove that $\{z_n \}_{n \in \Bbb Z} \in \ell^p(\Bbb Z),$ for $p \in [1,\infty).$

Show that there exists $M \gt 0$ such that for all $f \in S,$ $\|f\|_{\infty} \leq M \|f\|_2.$

$L^4$-norm of a random variable. Why is it computed like that?

Volterra integral operator with operator-valued kernel

$f\in L^\infty(\mathbb{R}^d)$ has uniform element iff $\Vert\tau_h f-f\Vert_\infty\to0$

Lower semi-continuity of the convolution of two nonnegative functions

If $X\subset L^1$ is a closed vector space and $X\subset \bigcup_{1<p\leq\infty} L^p$ then $X\subset L^q$ for some $q>1$.

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