List questions from banach-spaces

Published on 10 Apr 2026 - 8:04

37

Views

Existence of an element in the infinite dimensional normed linear space?

Published on 11 Apr 2026 - 21:33

467

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If a subspace of $L^p\cap L^q$ is closed with respect to both norms, the norms are equivalent on this subspace

Published on 11 Oct 2015 - 18:22

107

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Limit points of same sequence in different norm

Published on 10 Apr 2026 - 19:06

3.5k

Views

Subderivative of $ ||Au||_{L^{\infty}} $ to Compute Proximal Operator / Prox Operator

Published on 12 Oct 2015 - 14:12

166

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A peculiar characterization of open balls in a Banach space

Published on 02 Apr 2026 - 12:29

146

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Outline of Generic Separable Banach Spaces don't have a Schauder Basis

Published on 29 Mar 2026 - 22:12

276

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Coordinate projections in $l^p$ are Lipschitz continuous

Published on 09 Apr 2026 - 10:17

1k

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Contractive composite function

Published on 09 Mar 2026 - 5:46

278

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Let $X$ be a Banach space, and $B_1\supseteq B_2 \supseteq\cdots $ . Show that $\bigcap\limits_{i=1}^\infty B_i\neq\emptyset$

Published on 13 Oct 2015 - 16:04

215

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What is an example of nested bounded convex and closet sequence of set in a Banach space with empty intersection?

Published on 13 Oct 2015 - 16:36

71

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To show Banach Operator Norm's equivalence

Published on 01 Mar 2026 - 17:49

3.8k

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$C[0,1]$ with $L^1$ norm is not Banach space.

Published on 18 Mar 2026 - 23:47

84

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Two infinite dimensional spaces whose Banach-Mazur distance equal to 1(details in the proof)

Published on 12 Apr 2026 - 0:29

69

Views

$L(\bigoplus_{i\in I} H_i)\cong \prod_{i\in I}L(H_i)$ as Banach spaces?

Published on 07 Apr 2026 - 13:11

List Question

Doubt in the proof of Banach Alaoglu Theorem

Existence of an element in the infinite dimensional normed linear space?

If a subspace of $L^p\cap L^q$ is closed with respect to both norms, the norms are equivalent on this subspace

Limit points of same sequence in different norm

Subderivative of $ ||Au||_{L^{\infty}} $ to Compute Proximal Operator / Prox Operator

A peculiar characterization of open balls in a Banach space

Outline of Generic Separable Banach Spaces don't have a Schauder Basis

Coordinate projections in $l^p$ are Lipschitz continuous

Contractive composite function

Let $X$ be a Banach space, and $B_1\supseteq B_2 \supseteq\cdots $ . Show that $\bigcap\limits_{i=1}^\infty B_i\neq\emptyset$

What is an example of nested bounded convex and closet sequence of set in a Banach space with empty intersection?

To show Banach Operator Norm's equivalence

$C[0,1]$ with $L^1$ norm is not Banach space.

Two infinite dimensional spaces whose Banach-Mazur distance equal to 1(details in the proof)

$L(\bigoplus_{i\in I} H_i)\cong \prod_{i\in I}L(H_i)$ as Banach spaces?

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