List questions from lp-spaces

Published on 30 Nov 2018 - 11:04

153

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Sequence of functions on $\mathcal{L}^1([0,1])$ with $\lim_{n\rightarrow \infty}||f_n||_1=0$ but $\sup\{f_n(x): n\in\mathbf{Z}^+\}=\infty$?

Published on 27 Mar 2026 - 6:16

198

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If $X_n\to X$ in $L^p$, is $E(X_n^p)\to E(X^p)$ true?

Published on 02 Dec 2018 - 11:37

61

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showing $f=g$ a.e. given $f_n\to f$ uniformly and $f_n\to g$ in $L^p(\Bbb R)$

Published on 02 Dec 2018 - 15:05

161

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weighted norm modification

Published on 02 Dec 2018 - 19:18

83

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Function $f$ from $L^2[0,1]$ such that $\int \limits_0^1 f(x)g(x)dx = g(0)$, where $g$ is polynomial.

Published on 28 Mar 2026 - 9:45

76

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Generated space by the harmonic oscillators $e^{iw}$.

Published on 26 Mar 2026 - 6:19

61

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Unicity of the projection on a closed convex subset of $L^p$

Published on 25 Mar 2026 - 14:46

141

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Subset of $\ell^2$ with distance property

Published on 28 Mar 2026 - 11:33

395

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Applications of $L_p$ spaces

Published on 25 Mar 2026 - 12:37

233

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Calculating the norm of a specific bounded linear functional

Published on 06 Dec 2018 - 22:01

107

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Unique functional $F$ on $\ell_q(\mathbb{N})$ extending $f$ and satisfying $\|F\|=\|f\|$

Published on 07 Dec 2018 - 10:32

25

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Sufficient condition for $L^\infty$ distance bound

Published on 08 Dec 2018 - 0:29

350

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Given an averaging operator $A: l_p \rightarrow l_p$, why $A$ is not compact

Published on 25 Mar 2026 - 16:01

82

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function in Lp spaces

Published on 09 Dec 2018 - 18:19

List Question

The map $L^\infty$ to $(L^1)^*$ is not injective in this measure space?

Sequence of functions on $\mathcal{L}^1([0,1])$ with $\lim_{n\rightarrow \infty}||f_n||_1=0$ but $\sup\{f_n(x): n\in\mathbf{Z}^+\}=\infty$?

If $X_n\to X$ in $L^p$, is $E(X_n^p)\to E(X^p)$ true?

showing $f=g$ a.e. given $f_n\to f$ uniformly and $f_n\to g$ in $L^p(\Bbb R)$

weighted norm modification

Function $f$ from $L^2[0,1]$ such that $\int \limits_0^1 f(x)g(x)dx = g(0)$, where $g$ is polynomial.

Generated space by the harmonic oscillators $e^{iw}$.

Unicity of the projection on a closed convex subset of $L^p$

Subset of $\ell^2$ with distance property

Applications of $L_p$ spaces

Calculating the norm of a specific bounded linear functional

Unique functional $F$ on $\ell_q(\mathbb{N})$ extending $f$ and satisfying $\|F\|=\|f\|$

Sufficient condition for $L^\infty$ distance bound

Given an averaging operator $A: l_p \rightarrow l_p$, why $A$ is not compact

function in Lp spaces

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