List questions from dual-spaces

Published on 24 Mar 2026 - 23:59

380

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Is the dual to $C^1[0,1]$ separable?

Published on 22 Mar 2026 - 7:12

78

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Prove that $(V_{1} \times .......\times V_{m})'$ and $V'_{1} \times .......\times V'_m$ are isomorphic vector spaces

Published on 01 Jun 2018 - 15:44

72

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Special Case of the Riesz Representation Theorem

Published on 22 Mar 2026 - 15:19

2.3k

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Natural isomorphism between a vector space and its double dual

Published on 05 Jun 2018 - 8:14

10.8k

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Annihilator of a vector space $V$ is the zero subspace of $V^*$

Published on 10 Jun 2018 - 21:38

721

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Multiplying Vectors and Covectors

Published on 11 Jun 2018 - 16:42

417

Views

When are $V$ and $V^{*}$ canonically isomorphic?

Published on 13 Jun 2018 - 7:48

118

Views

Norm of linear functional in $l_1$

Published on 16 Jun 2018 - 21:58

814

Views

Let $X$ be a normed space and $Y$ be a proper dense linear subspace of $X$. Then how to show $Y^\cong X^$?

Published on 18 Jun 2018 - 22:15

437

Views

How the dual basis is used to transform a vector to a scalar?

Published on 24 Jun 2018 - 11:31

73

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show that there exists a basis $ \ \mathcal{B}'=\{e_1',e_2',......, e_n' \} \ \ of \ \ V $ such that $ \ G(e_i,e_j')=\delta^i_j \ $

Published on 26 Jun 2018 - 2:44

996

Views

Sheldon Axler 3.109 : How to interpret " range T' = $(null\;T)^0$ "?

Published on 19 Mar 2026 - 13:31

509

Views

Kronecker delta indexing rules: How the left side indices are calculated?

Published on 04 Jul 2018 - 17:36

29

Views

Space and it's space of linear functions are of same dimensionality

Published on 05 Jul 2018 - 17:43

List Question

Dual space/isomorphism

Is the dual to $C^1[0,1]$ separable?

Prove that $(V_{1} \times .......\times V_{m})'$ and $V'_{1} \times .......\times V'_m$ are isomorphic vector spaces

Special Case of the Riesz Representation Theorem

Natural isomorphism between a vector space and its double dual

Annihilator of a vector space $V$ is the zero subspace of $V^*$

Multiplying Vectors and Covectors

When are $V$ and $V^{*}$ canonically isomorphic?

Norm of linear functional in $l_1$

Let $X$ be a normed space and $Y$ be a proper dense linear subspace of $X$. Then how to show $Y^\cong X^$?

How the dual basis is used to transform a vector to a scalar?

show that there exists a basis $ \ \mathcal{B}'=\{e_1',e_2',......, e_n' \} \ \ of \ \ V $ such that $ \ G(e_i,e_j')=\delta^i_j \ $

Sheldon Axler 3.109 : How to interpret " range T' = $(null\;T)^0$ "?

Kronecker delta indexing rules: How the left side indices are calculated?

Space and it's space of linear functions are of same dimensionality

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