List questions from lp-spaces

Published on 16 Apr 2026 - 2:08

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Bounded subsequence in Sobolev Space

Published on 24 Apr 2026 - 23:07

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Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $

Published on 12 Apr 2026 - 22:17

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In $\ell^p$, if an operator commutes with left shift, it is continuous?

Published on 09 Apr 2026 - 6:21

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$\ell^p(I)$ space and a dense set of this space

Published on 15 Apr 2026 - 12:52

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Is $L^p \cap L^q$ dense in $L^r$?

Published on 16 Apr 2026 - 11:06

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Assume $\int_{D}fgdx=0\forall g\in C_{c}^{\infty}\left(D\right)$. Then $f = 0$ a.e. on D.

Published on 16 Apr 2026 - 6:06

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Fractional Sobolev embedding into $L^\infty$

Published on 25 Apr 2026 - 0:54

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Compact kernel operator on $L^p$ space

Published on 08 Apr 2026 - 19:14

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is the following set complete in $l_p$?

Published on 12 Apr 2026 - 2:59

50

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Bounded derivative on interval implies almost everywhere boundedness?

Published on 18 Apr 2026 - 4:49

142

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bounded linear functional on $\ell^{1}$, and its relation to $\ell^{\infty}$

Published on 12 Apr 2026 - 3:00

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Why is $l^\infty$ not separable?

Published on 14 Apr 2026 - 11:28

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How is the $l^p$ space separable?

Published on 13 Apr 2026 - 6:57

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Is $\{f\in H^1;\;\int f=0\}$ dense in $\{f\in L^2;\;\int f=0\}$?

Published on 25 Apr 2026 - 1:00

List Question

Show $T:G\rightarrow L^1(G)$ by $y\mapsto f(y\cdot)$ is continuous for fixed $f\in L^1(G)$

Bounded subsequence in Sobolev Space

Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $

In $\ell^p$, if an operator commutes with left shift, it is continuous?

$\ell^p(I)$ space and a dense set of this space

Is $L^p \cap L^q$ dense in $L^r$?

Assume $\int_{D}fgdx=0\forall g\in C_{c}^{\infty}\left(D\right)$. Then $f = 0$ a.e. on D.

Fractional Sobolev embedding into $L^\infty$

Compact kernel operator on $L^p$ space

is the following set complete in $l_p$?

Bounded derivative on interval implies almost everywhere boundedness?

bounded linear functional on $\ell^{1}$, and its relation to $\ell^{\infty}$

Why is $l^\infty$ not separable?

How is the $l^p$ space separable?

Is $\{f\in H^1;\;\int f=0\}$ dense in $\{f\in L^2;\;\int f=0\}$?

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