Question

Let $M\subseteq X$ be a maximal subspace of the normed space $X$. Is there a functional $f\in X^*$ such that $\ker f = M$?

score 69 · Answer 1 · 2022-04-23 15:42:09

69

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Let $M\subseteq X$ be a maximal subspace of the normed space $X$. Is there a functional $f\in X^*$ such that $\ker f = M$?

Published on 23 Apr 2022 - 15:42

score 435 · Answer 2 · 2022-04-23 21:57:26

435

Views

Clarification on definition of representation of $\mathrm{Hom}(V,W)$

Published on 23 Apr 2022 - 21:57

score 146 · Answer 3 · 2022-04-25 15:47:17

146

Views

Kernel of a function in the dual space

Published on 25 Apr 2022 - 15:47

score 95 · Answer 4 · 2022-04-26 01:43:00

95

Views

Proof for $(Z^\perp)^{\perp} = Z$

Published on 26 Apr 2022 - 1:43

score 114 · Answer 5 · 2022-04-27 09:43:59

114

Views

How to prove if the following is a dual vector?

Published on 27 Apr 2022 - 9:43

score 305 · Answer 6 · 2022-04-28 11:43:38

305

Views

Irreducible dual representation on finite dimensional vector space

Published on 28 Apr 2022 - 11:43

score 154 · Answer 7 · 2026-03-28 02:21:24

154

Views

What's the problem with the evaluation map not being continuous?

Published on 28 Mar 2026 - 2:21

score 127 · Answer 8 · 2022-05-12 12:04:41

127

Views

Is there a very small gap or no gap in this proof? ("Linear Algebra Done Right 3rd Edition" by Sheldon Axler.)

Published on 12 May 2022 - 12:04

score 65 · Answer 9 · 2022-05-14 18:05:13

65

Views

Proof about dual space

Published on 14 May 2022 - 18:05

score 242 · Answer 10 · 2026-03-27 19:32:37

242

Views

Exercise 3.F.5 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

Published on 27 Mar 2026 - 19:32

score 72 · Answer 11 · 2022-05-25 00:55:09

72

Views

Exercise 3.F.35 Show that $(\mathcal{P}(\mathbb{R}))'$ and $\mathbb{R}^\infty$ are isomorphic (Linear Algebra Done Right 3rd Edition by Sheldon Axler)

Published on 25 May 2022 - 0:55

score 90 · Answer 12 · 2026-03-27 19:31:57

90

Views

A canonical isomorphism from $V$ to $W$.

Published on 27 Mar 2026 - 19:31

score 403 · Answer 13 · 2022-05-27 02:34:55

403

Views

Exercise 3.F.28 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

Published on 27 May 2022 - 2:34

score 48 · Answer 14 · 2022-05-30 10:54:01

48

Views

What is the significance / use of $\ell_p$'s dual space?

Published on 30 May 2022 - 10:54

score 111 · Answer 15 · 2022-06-02 20:01:15

111

Views

What is the natural morphism between an $R$ module and its bidual?

Published on 02 Jun 2022 - 20:01

List Question

Let $M\subseteq X$ be a maximal subspace of the normed space $X$. Is there a functional $f\in X^*$ such that $\ker f = M$?

Clarification on definition of representation of $\mathrm{Hom}(V,W)$

Kernel of a function in the dual space

Proof for $(Z^\perp)^{\perp} = Z$

How to prove if the following is a dual vector?

Irreducible dual representation on finite dimensional vector space

What's the problem with the evaluation map not being continuous?

Is there a very small gap or no gap in this proof? ("Linear Algebra Done Right 3rd Edition" by Sheldon Axler.)

Proof about dual space

Exercise 3.F.5 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

Exercise 3.F.35 Show that $(\mathcal{P}(\mathbb{R}))'$ and $\mathbb{R}^\infty$ are isomorphic (Linear Algebra Done Right 3rd Edition by Sheldon Axler)

A canonical isomorphism from $V$ to $W$.

Exercise 3.F.28 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler.

What is the significance / use of $\ell_p$'s dual space?

What is the natural morphism between an $R$ module and its bidual?

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