List questions from lp-spaces

Published on 10 Apr 2026 - 2:20

106

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Can someone explain why $\| \cdot \|_p, p = \frac{1}{2}$ isn't a norm?

Published on 14 Apr 2026 - 9:02

113

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Norm inequality proof.

Published on 10 Apr 2026 - 19:35

329

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show that a certain bounded linear operator does not exist

Published on 12 Apr 2026 - 5:06

414

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Infinite matrix SIGNIFICANT PROGRESS BUT STUCK defines compact operator on $ l^2 $

Published on 17 Apr 2026 - 17:55

125

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HALF SOLVED: A specific problem in linear operator on $ l^1 $ and $ l^{\infty} $

Published on 11 Apr 2026 - 4:44

2.7k

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Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable

Published on 16 Apr 2026 - 16:32

44

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Is $\mathscr{C}(K)$ a subspace of every $L^p(K)$, if $K$ is compact?

Published on 13 Apr 2026 - 20:10

2.7k

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If all $L^p$ norms are bounded then the $L^\infty$ is bounded

Published on 15 Apr 2026 - 22:21

66

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Example of bounded function in $L^1[a,b]$ but not in $L^2[a,b]$

Published on 14 Apr 2026 - 4:28

158

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Proving that the point spectrum of the right shift operator on $\mathscr{l}^2(\mathbb{Z})$ is empty.

Published on 14 Apr 2026 - 4:02

143

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$L^p$ and $\mathscr{l}^p$ embeddings and norm inequalities

Published on 15 Apr 2026 - 16:43

142

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$L_{\infty}$ not separable: Find nested subsets of $\Omega \subset \mathbb{R}^d$ with positive finite Lebesgue measure?

Published on 14 Apr 2026 - 6:48

1.1k

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Cauchy sequence in $L^p(\mu)$

Published on 17 Apr 2026 - 9:37

47

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$L_p$ approximation of $f \in L_p$ is also in $L_p$.

Published on 16 Apr 2026 - 5:51

List Question

Understanding the embedding of $W^{\infty, 2}$

Can someone explain why $\| \cdot \|_p, p = \frac{1}{2}$ isn't a norm?

Norm inequality proof.

show that a certain bounded linear operator does not exist

Infinite matrix SIGNIFICANT PROGRESS BUT STUCK defines compact operator on $ l^2 $

HALF SOLVED: A specific problem in linear operator on $ l^1 $ and $ l^{\infty} $

Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable

Is $\mathscr{C}(K)$ a subspace of every $L^p(K)$, if $K$ is compact?

If all $L^p$ norms are bounded then the $L^\infty$ is bounded

Example of bounded function in $L^1[a,b]$ but not in $L^2[a,b]$

Proving that the point spectrum of the right shift operator on $\mathscr{l}^2(\mathbb{Z})$ is empty.

$L^p$ and $\mathscr{l}^p$ embeddings and norm inequalities

$L_{\infty}$ not separable: Find nested subsets of $\Omega \subset \mathbb{R}^d$ with positive finite Lebesgue measure?

Cauchy sequence in $L^p(\mu)$

$L_p$ approximation of $f \in L_p$ is also in $L_p$.

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