List questions from lp-spaces

28

Views

Is $M = \{ f \in L_2[1,\infty) : \int_1^{\infty}\frac{f(t)}{t}dt = 0 \}$ a closed subspace in $L_2[1,\infty)$?

Published on 26 Apr 2020 - 19:02

158

Views

Let $f_n=\chi_{[n,n+1]}$. Does $f_n$ converge weakly to $0$ in $L^1(\mathbb{R})$?

Published on 27 Apr 2020 - 14:05

301

Views

$L^p$ spaces are always connected?

Published on 27 Apr 2020 - 14:41

249

Views

Under what conditions can $L^p(X,\sigma,\mu)$ be an inner product space for $p\neq 2$?

Published on 05 Apr 2026 - 23:28

397

Views

Example of $L_1$ and $L_p$ function whose convolution is not in $L_1$

Published on 30 Mar 2026 - 6:45

133

Views

Young inequality: Generalization on $\mathbb{T}$ space.

Published on 25 Mar 2026 - 6:09

50

Views

Clarifying a step in the equality case of the Hölders inequalite

Published on 25 Mar 2026 - 16:13

392

Views

Computing the $L^p$ norm of an integral operator

Published on 01 Apr 2026 - 22:27

158

Views

about $l^p$ space and qoutient space

Published on 26 Mar 2026 - 6:26

258

Views

What is the $\sigma(L^1,L^\infty)$-topology?

Published on 29 Apr 2020 - 16:12

65

Views

Weak limit points of an $L^1$-space

Published on 25 Mar 2026 - 22:03

33

Views

If $\tau$ is weakly continuous and $(Z_n)$ is a sequence with limit point $Z$ on $L^1$ and $Z_n\le Y$, then $Z\le Y$

Published on 30 Apr 2020 - 14:02

189

Views

How can I prove $L^p(\Omega,\mathcal{E})$ is separable without assuming $\Omega=\mathbb{R}^N$?

Published on 30 Apr 2020 - 14:33

551

Views

Containment of $L^P$ spaces.

Published on 01 May 2020 - 13:49

46

Views

Find an isometry $j: l_{\infty} \rightarrow B\left(L_{p}[0,1]\right)$

Published on 26 Mar 2026 - 8:04

List Question

Is $M = \{ f \in L_2[1,\infty) : \int_1^{\infty}\frac{f(t)}{t}dt = 0 \}$ a closed subspace in $L_2[1,\infty)$?

Let $f_n=\chi_{[n,n+1]}$. Does $f_n$ converge weakly to $0$ in $L^1(\mathbb{R})$?

$L^p$ spaces are always connected?

Under what conditions can $L^p(X,\sigma,\mu)$ be an inner product space for $p\neq 2$?

Example of $L_1$ and $L_p$ function whose convolution is not in $L_1$

Young inequality: Generalization on $\mathbb{T}$ space.

Clarifying a step in the equality case of the Hölders inequalite

Computing the $L^p$ norm of an integral operator

about $l^p$ space and qoutient space

What is the $\sigma(L^1,L^\infty)$-topology?

Weak limit points of an $L^1$-space

If $\tau$ is weakly continuous and $(Z_n)$ is a sequence with limit point $Z$ on $L^1$ and $Z_n\le Y$, then $Z\le Y$

How can I prove $L^p(\Omega,\mathcal{E})$ is separable without assuming $\Omega=\mathbb{R}^N$?

Containment of $L^P$ spaces.

Find an isometry $j: l_{\infty} \rightarrow B\left(L_{p}[0,1]\right)$

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