List questions from lp-spaces

Published on 15 May 2026 - 15:10

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How can I fix my proof that $\ell^1$ is complete?

Published on 10 Apr 2026 - 20:45

76

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$\ell_p\subset\ell_q$ proof verification

Published on 15 Apr 2026 - 20:55

95

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Notations in Functional Analysis

Published on 09 Apr 2026 - 4:31

190

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On the continuity of Nemytskii operators

Published on 14 Apr 2026 - 2:06

113

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Understanding the Proof of Kolmogorov-Riesz Theorem

Published on 08 Apr 2026 - 21:26

23

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Set inclusion between space of probabilities

Published on 18 Apr 2026 - 4:20

151

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Complex interpolation of weighted $L^p$ spaces

Published on 11 May 2026 - 0:50

360

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$ f_n(x) := n^{\frac{1}{p}} \chi_{[0,1]}(n x) $ weakly converges to $0$ for $p>1$, but not for $p=1$

Published on 16 Apr 2026 - 11:46

54

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For 1≤p<q≤$\infty$, show that $L^{p}(\mathbb{Z},\mu) \subset L^{q}(\mathbb{Z},\mu)$, $\mu$ being the counting measure.

Published on 15 Apr 2026 - 19:05

50

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log-convexity of the operator norm

Published on 13 Apr 2026 - 7:31

179

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Continuous Approximation of Lp function on $\mathbf{R}^n$

Published on 12 Apr 2026 - 14:47

56

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Equivalence of two convergence statements in $L^p$ spaces

Published on 11 Apr 2026 - 2:39

41

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Convergence of Norm Sequences

Published on 12 Apr 2026 - 1:22

63

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Projecting unit $\ell_p$ vector onto $\ell_2$ and measuring distortion in $\ell_p$

Published on 15 May 2026 - 10:21

List Question

Weak derivative of Extension of a function in sobolev space

How can I fix my proof that $\ell^1$ is complete?

$\ell_p\subset\ell_q$ proof verification

Notations in Functional Analysis

On the continuity of Nemytskii operators

Understanding the Proof of Kolmogorov-Riesz Theorem

Set inclusion between space of probabilities

Complex interpolation of weighted $L^p$ spaces

$ f_n(x) := n^{\frac{1}{p}} \chi_{[0,1]}(n x) $ weakly converges to $0$ for $p>1$, but not for $p=1$

For 1≤p<q≤$\infty$, show that $L^{p}(\mathbb{Z},\mu) \subset L^{q}(\mathbb{Z},\mu)$, $\mu$ being the counting measure.

log-convexity of the operator norm

Continuous Approximation of Lp function on $\mathbf{R}^n$

Equivalence of two convergence statements in $L^p$ spaces

Convergence of Norm Sequences

Projecting unit $\ell_p$ vector onto $\ell_2$ and measuring distortion in $\ell_p$

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