Question

Are there spaces "smaller" than $c_0$ whose dual is $\ell^1$?

score 1.7k · Answer 1 · 2014-10-10 03:31:57

1.7k

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Are there spaces "smaller" than $c_0$ whose dual is $\ell^1$?

Published on 10 Oct 2014 - 3:31

score 1.5k · Answer 2 · 2014-12-21 02:20:01

1.5k

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Dual of $\ell^p$ Direct sum

Published on 21 Dec 2014 - 2:20

score 413 · Answer 3 · 2026-03-23 10:11:03

413

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Converting mixed L1/L2 problem with Constraints to Quadratic Program

Published on 23 Mar 2026 - 10:11

score 140 · Answer 4 · 2026-03-23 23:31:57

140

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Is what's a vector and covector subjective?

Published on 23 Mar 2026 - 23:31

score 59 · Answer 5 · 2026-03-21 21:54:06

59

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How to show that $\lambda\in V^{**}$ is in the image of $V$ iff it is weak-* continuous?

Published on 21 Mar 2026 - 21:54

score 29 · Answer 6 · 2026-03-09 20:33:11

29

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Why induced linear transformations of bilinear function are duals of each other?

Published on 09 Mar 2026 - 20:33

score 177 · Answer 7 · 2019-10-17 12:37:44

177

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Dual Space and Dual Basis

Published on 17 Oct 2019 - 12:37

score 25 · Answer 8 · 2026-03-01 14:17:18

25

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Is $\text{ball}_{R}(X^{\ast})\cap\bigcap_{i\in I}\{x^{\ast}\in X^{\ast} | \ |x^{\ast}(x_i)|\leq r_i\}$ norm (or weak*) connected?

Published on 01 Mar 2026 - 14:17

score 65 · Answer 9 · 2019-10-20 23:54:58

65

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Showing that the dual space of $H^{s,p}(\mathbb{R}^n) $ is $H^{-s,p'}(\mathbb{R}^n)$ with $\frac{1}{p}+\frac{1}{p'}=1$

Published on 20 Oct 2019 - 23:54

score 253 · Answer 10 · 2019-10-30 19:19:31

253

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Example where $(V^)^\neq V$?

Published on 30 Oct 2019 - 19:19

score 57 · Answer 11 · 2019-10-31 13:00:25

57

Views

Let $(E,\|\cdot\|)$ be an Euclidean vector space. Prove that if $f: E \to E$ is linear then $f$ is continuous

Published on 31 Oct 2019 - 13:00

score 654 · Answer 12 · 2019-11-02 19:40:58

654

Views

Dual Space and Bidual

Published on 02 Nov 2019 - 19:40

score 358 · Answer 13 · 2019-11-03 01:07:49

358

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Proving that $\operatorname{Ann}(W)$ is a subspace of $\operatorname{Hom}(V,F)$ and further $\dim \operatorname{Ann}(W) = \dim V-\dim W$

Published on 03 Nov 2019 - 1:07

score 107 · Answer 14 · 2019-11-03 06:23:05

107

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An exercise of advanced analysis with the sign function

Published on 03 Nov 2019 - 6:23

score 54 · Answer 15 · 2019-11-03 18:10:08

54

Views

Regarding relation between dimension of dual space of normed linear space X and dimension of X.

Published on 03 Nov 2019 - 18:10

List Question

Are there spaces "smaller" than $c_0$ whose dual is $\ell^1$?

Dual of $\ell^p$ Direct sum

Converting mixed L1/L2 problem with Constraints to Quadratic Program

Is what's a vector and covector subjective?

How to show that $\lambda\in V^{**}$ is in the image of $V$ iff it is weak-* continuous?

Why induced linear transformations of bilinear function are duals of each other?

Dual Space and Dual Basis

Is $\text{ball}_{R}(X^{\ast})\cap\bigcap_{i\in I}\{x^{\ast}\in X^{\ast} | \ |x^{\ast}(x_i)|\leq r_i\}$ norm (or weak*) connected?

Showing that the dual space of $H^{s,p}(\mathbb{R}^n) $ is $H^{-s,p'}(\mathbb{R}^n)$ with $\frac{1}{p}+\frac{1}{p'}=1$

Example where $(V^)^\neq V$?

Let $(E,\|\cdot\|)$ be an Euclidean vector space. Prove that if $f: E \to E$ is linear then $f$ is continuous

Dual Space and Bidual

Proving that $\operatorname{Ann}(W)$ is a subspace of $\operatorname{Hom}(V,F)$ and further $\dim \operatorname{Ann}(W) = \dim V-\dim W$

An exercise of advanced analysis with the sign function

Regarding relation between dimension of dual space of normed linear space X and dimension of X.

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