List questions from dual-spaces

Published on 25 Feb 2012 - 10:58

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A Banach space is reflexive if and only if its dual is reflexive

Published on 23 Feb 2026 - 8:25

28.4k

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Motivation to understand double dual space

Published on 13 Jul 2012 - 21:18

3.5k

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$C_0(X)$ is not the dual of a complete normed space

Published on 09 Oct 2012 - 20:31

254

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Dimension of the dual code and the rank-nullity theorem

Published on 06 Nov 2012 - 1:02

2.7k

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Is any Banach space a dual space?

Published on 21 Nov 2012 - 15:27

259

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How to construct an "explicit" element of $(\ell^\infty(\mathbb N))^* \setminus \ell^1(\mathbb N)$?

Published on 24 Jan 2013 - 16:38

1.5k

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$S\subseteq V \Rightarrow \text{span}(S)\cong S^{00}$

Published on 24 Jan 2013 - 19:56

501

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Motivation for the development of the double dual of a vector space

Published on 03 Feb 2013 - 6:43

208

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Relation: Module structure on the dual and braiding?

Published on 01 Aug 2020 - 13:02

918

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How is the isomorphism between a vector space and its dual not natural?

Published on 01 Aug 2020 - 18:24

194

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Further interesting examples? Obtaining (co)monoids from dual objects

Published on 03 Aug 2020 - 11:03

64

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Clarification about the definition of subgradient

Published on 26 Mar 2026 - 4:16

59

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Let $w$ be a positive continuous function for which $\int_0^1 w(x)dx = \int_0^1 x^2w(x)dx = 1$. Prove that $\int_0^1 xw(x)dx < 1$.

Published on 26 Mar 2026 - 17:50

80

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If Ker $T\subset$ Ker $T^*$ then $\exists C>0$ such that $\langle Tx,x\rangle_{X'\times X}\geq -C\|Tx\|_{X}^2$

Published on 08 Aug 2020 - 6:27

List Question

Banach Spaces - How can $B,B',B'', B''', B'''',B''''',\ldots$ behave?

A Banach space is reflexive if and only if its dual is reflexive

Motivation to understand double dual space

$C_0(X)$ is not the dual of a complete normed space

Dimension of the dual code and the rank-nullity theorem

Is any Banach space a dual space?

How to construct an "explicit" element of $(\ell^\infty(\mathbb N))^* \setminus \ell^1(\mathbb N)$?

$S\subseteq V \Rightarrow \text{span}(S)\cong S^{00}$

Motivation for the development of the double dual of a vector space

Relation: Module structure on the dual and braiding?

How is the isomorphism between a vector space and its dual not natural?

Further interesting examples? Obtaining (co)monoids from dual objects

Clarification about the definition of subgradient

Let $w$ be a positive continuous function for which $\int_0^1 w(x)dx = \int_0^1 x^2w(x)dx = 1$. Prove that $\int_0^1 xw(x)dx < 1$.

If Ker $T\subset$ Ker $T^*$ then $\exists C>0$ such that $\langle Tx,x\rangle_{X'\times X}\geq -C\|Tx\|_{X}^2$

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