List questions from lp-spaces

Published on 11 Apr 2026 - 6:07

63

Views

Is this claim about mapping closed discrete sets into open sets true for $l^2$?

Published on 10 Apr 2026 - 16:27

884

Views

$L^{1}$ and $L^{\infty}$ norms are not equivalent on compact sets

Published on 13 Apr 2026 - 6:41

613

Views

Completeness of continuous functions space under $L^{1}$ norm

Published on 17 Apr 2026 - 10:11

53

Views

Are there the same conclusions in quaternion

Published on 09 Apr 2026 - 8:36

168

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Question on the spectral theorem for unitary operators.

Published on 10 Apr 2026 - 16:13

176

Views

Uniform convergence on compact sets and convergence on $L^1$

Published on 05 May 2026 - 23:52

53

Views

A question on the size of the topology with respect to the sequential convergence.

Published on 06 May 2026 - 3:12

58

Views

Is $(-y,x)/\sqrt{x^2+y^2}$ in $[W^{1,\infty}([0,1]^2)]^2$

Published on 16 Apr 2026 - 3:50

93

Views

Exercise regarding pointwise convergence and $L^p$ convergence

Published on 17 Apr 2026 - 22:41

134

Views

$\|x\|_{p} \rightarrow\|x\|_{\infty}$ as $p \rightarrow \infty$

Published on 16 Apr 2026 - 3:06

71

Views

How is the topology on $\ell^2$ and $\ell^p$ spaces called?

Published on 14 Apr 2026 - 17:44

83

Views

How to prove a claim about mapping closed sets to subsets of open sets of $\ell^2$

Published on 14 Apr 2026 - 13:18

63

Views

weak convergence of a function in $L^2$

Published on 06 May 2026 - 12:01

64

Views

Show that the map $\varphi : \chi \to \psi_{\chi}$ is continuous.

Published on 13 Apr 2026 - 9:10

List Question

When a space is NOT locally compact, does it have dense remainder in its compactification?

Is this claim about mapping closed discrete sets into open sets true for $l^2$?

$L^{1}$ and $L^{\infty}$ norms are not equivalent on compact sets

Completeness of continuous functions space under $L^{1}$ norm

Are there the same conclusions in quaternion

Question on the spectral theorem for unitary operators.

Uniform convergence on compact sets and convergence on $L^1$

A question on the size of the topology with respect to the sequential convergence.

Is $(-y,x)/\sqrt{x^2+y^2}$ in $[W^{1,\infty}([0,1]^2)]^2$

Exercise regarding pointwise convergence and $L^p$ convergence

$\|x\|_{p} \rightarrow\|x\|_{\infty}$ as $p \rightarrow \infty$

How is the topology on $\ell^2$ and $\ell^p$ spaces called?

How to prove a claim about mapping closed sets to subsets of open sets of $\ell^2$

weak convergence of a function in $L^2$

Show that the map $\varphi : \chi \to \psi_{\chi}$ is continuous.

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