List questions from lp-spaces

Published on 23 Mar 2026 - 18:27

357

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Understanding the essential range

Published on 20 Mar 2026 - 9:46

192

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Problem 1.70 of Megginson's "An Introduction to Banach Space Theory"

Published on 22 Mar 2026 - 5:15

82

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Showing a sequence is in $\ell^1$

Published on 22 Mar 2026 - 9:17

1.2k

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How to conclude that $\ell_\infty$ is not separable from this exercise?

Published on 22 Mar 2026 - 6:06

89

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Calculating the gradient in $L^p$ space when $0<p<1$ and the uderlying set is discrete and finite

Published on 21 Mar 2026 - 4:48

102

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$f_{n} \in L^{p}(X),$ such that $\lVert f_{n}-f_{n+1}\rVert_{p} \leq \frac{1}{n^2}$. Prove $f_{n}$ converges a.e.

Published on 21 Mar 2026 - 12:26

122

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Find a sequence converging in distribution but not weakly

Published on 21 Mar 2026 - 10:49

65

Views

Elementary use of Hölder inequality

Published on 20 Mar 2026 - 9:07

324

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Identify $\operatorname{co}(\{e_n:n\in\mathbb N\})$ and $\overline{\operatorname{co}}(\{e_n : n\in\mathbb N\})$ in $c_0$ and $\ell^p$

Published on 20 Mar 2026 - 8:54

70

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Normed bounded sequence of $L^2[0,1]$

Published on 20 Mar 2026 - 5:16

163

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Sequence in $B[0,1]\subset L^2[0,1]$ which has no convergent subseqence.

Published on 22 Mar 2026 - 14:17

101

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Checking that a function is in $L^p(\mathbb{C})$

Published on 22 Mar 2026 - 17:38

542

Views

Weak and strong compactness in $L^2$

Published on 22 Mar 2026 - 9:40

76

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Fourier Series on $L^1\left(\left[0,1\right)\right)\cap C\left(\left[0,1\right)\right)$

Published on 20 Mar 2026 - 4:07

List Question

Absolutely continuous functions are dense in $L^1$

Understanding the essential range

Problem 1.70 of Megginson's "An Introduction to Banach Space Theory"

Showing a sequence is in $\ell^1$

How to conclude that $\ell_\infty$ is not separable from this exercise?

Calculating the gradient in $L^p$ space when $0<p<1$ and the uderlying set is discrete and finite

$f_{n} \in L^{p}(X),$ such that $\lVert f_{n}-f_{n+1}\rVert_{p} \leq \frac{1}{n^2}$. Prove $f_{n}$ converges a.e.

Find a sequence converging in distribution but not weakly

Elementary use of Hölder inequality

Identify $\operatorname{co}(\{e_n:n\in\mathbb N\})$ and $\overline{\operatorname{co}}(\{e_n : n\in\mathbb N\})$ in $c_0$ and $\ell^p$

Normed bounded sequence of $L^2[0,1]$

Sequence in $B[0,1]\subset L^2[0,1]$ which has no convergent subseqence.

Checking that a function is in $L^p(\mathbb{C})$

Weak and strong compactness in $L^2$

Fourier Series on $L^1\left(\left[0,1\right)\right)\cap C\left(\left[0,1\right)\right)$

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