Question

Double dual and tensor product for infinite dimensional spaces

score 48 · Answer 1 · 2024-02-29 16:41:07

48

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Double dual and tensor product for infinite dimensional spaces

Published on 29 Feb 2024 - 16:41

score 48 · Answer 2 · 2024-03-03 16:17:28

48

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Dual space of $L^p([0,1])$ for $0 < p < 1$.

Published on 03 Mar 2024 - 16:17

score 23 · Answer 3 · 2026-03-25 17:46:25

23

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Dual mappings - from U to V and from V to W

Published on 25 Mar 2026 - 17:46

score 74 · Answer 4 · 2024-03-15 03:16:23

74

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Why does there exist unique numbers $\varphi_1(v), \ldots, \varphi_m(v)$ such that $ Tv = \varphi_1(v)w_1 + \cdots + \varphi_m(v)w_m$?

Published on 15 Mar 2024 - 3:16

score 34 · Answer 5 · 2026-03-25 09:39:59

34

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Can $C_p^\infty(\mathbb{R}^n)$ be considered as a dual space of $T_p\mathbb{R}^n$, where $p\in \mathbb{R}^n$?

Published on 25 Mar 2026 - 9:39

score 72 · Answer 6 · 2024-03-21 03:48:00

72

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How do we know the space of distributions is "big"?

Published on 21 Mar 2024 - 3:48

score 105 · Answer 7 · 2026-03-26 06:20:35

105

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The dual $(L^\infty)^{*}$ is not $L^1$ by constructing example

Published on 26 Mar 2026 - 6:20

score 53 · Answer 8 · 2024-03-26 22:01:16

53

Views

Covectors, Metric Tensors and Unit Vectors

Published on 26 Mar 2024 - 22:01

score 140 · Answer 9 · 2024-03-31 05:18:30

140

Views

dual space of l2 with strange norm

Published on 31 Mar 2024 - 5:18

score 49 · Answer 10 · 2024-03-31 09:00:27

49

Views

$S \in \mathcal{L}(L^1(\Omega))$, find $T^* \in \mathcal{L}(L^\infty(\Omega))$ with $T^*g = Sg \forall g \in L^1(\Omega) \cap L^\infty(\Omega)$

Published on 31 Mar 2024 - 9:00

score 98 · Answer 11 · 2026-03-27 21:19:08

98

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Exercise 3.F.29(a) in "Linear Algebra Done Right 4th Edition" by Sheldon Axler.

Published on 27 Mar 2026 - 21:19

score 57 · Answer 12 · 2024-03-31 21:58:49

57

Views

How Can I Improve this Proof of Surjectivity between $V$ and $(V^\ast)^\ast$

Published on 31 Mar 2024 - 21:58

score 135 · Answer 13 · 2015-01-22 19:10:16

135

Views

Can these characterisations of finite dimensionality be proven equivalent without using a basis?

Published on 22 Jan 2015 - 19:10

score 1k · Answer 14 · 2026-03-27 21:19:31

1k

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dual of $L^\infty$ or $l^{\infty}$ spaces and characters of these spaces

Published on 27 Mar 2026 - 21:19

score 1.2k · Answer 15 · 2026-03-27 22:57:36

1.2k

Views

Can we always say, for finite-dimensional spaces, that there is no canonical isomorphism between $V$ and $V^*$?

Published on 27 Mar 2026 - 22:57

List Question

Double dual and tensor product for infinite dimensional spaces

Dual space of $L^p([0,1])$ for $0 < p < 1$.

Dual mappings - from U to V and from V to W

Why does there exist unique numbers $\varphi_1(v), \ldots, \varphi_m(v)$ such that $ Tv = \varphi_1(v)w_1 + \cdots + \varphi_m(v)w_m$?

Can $C_p^\infty(\mathbb{R}^n)$ be considered as a dual space of $T_p\mathbb{R}^n$, where $p\in \mathbb{R}^n$?

How do we know the space of distributions is "big"?

The dual $(L^\infty)^{*}$ is not $L^1$ by constructing example

Covectors, Metric Tensors and Unit Vectors

dual space of l2 with strange norm

$S \in \mathcal{L}(L^1(\Omega))$, find $T^* \in \mathcal{L}(L^\infty(\Omega))$ with $T^*g = Sg \forall g \in L^1(\Omega) \cap L^\infty(\Omega)$

Exercise 3.F.29(a) in "Linear Algebra Done Right 4th Edition" by Sheldon Axler.

How Can I Improve this Proof of Surjectivity between $V$ and $(V^\ast)^\ast$

Can these characterisations of finite dimensionality be proven equivalent without using a basis?

dual of $L^\infty$ or $l^{\infty}$ spaces and characters of these spaces

Can we always say, for finite-dimensional spaces, that there is no canonical isomorphism between $V$ and $V^*$?

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