List questions from hahn-banach-theorem

Published on 19 Mar 2026 - 11:07

55

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Showing that $\exists f \in X^*$ : $\|f\| = \frac{1}{d(x_0,Y)}, \; f(x_0) = 1$ and $f(y) = 0$.

Published on 19 Mar 2026 - 23:54

171

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Show that $x_0 \in \overline{\langle M \rangle } $ if and only if $f(x_0) = 0, \; \forall f \in X^* : f|_M = 0$.

Published on 20 Mar 2026 - 0:28

112

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Easy way to extend continous functional

Published on 22 Mar 2026 - 6:01

258

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How to prove that continuous convex functional on normed vector space must be lower bounded by some continuous affine functional?

Published on 19 Mar 2026 - 16:59

402

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(Hahn-Banach) Is a subadditive and positively homogeneous function continuous at $0$?

Published on 19 Mar 2026 - 15:23

415

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An "open-strict" Version of Hahn Banach Separation Theorem?

Published on 19 Mar 2026 - 18:16

672

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are linear functionals on C[0, 1] bounded and thus continuous

Published on 19 Mar 2026 - 23:37

836

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Is a Hahn-Banach extension always continuous?

Published on 22 Mar 2026 - 20:05

1.2k

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Corollary of the Hahn Banach theorem

Published on 22 Mar 2026 - 18:41

705

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Hahn Banach Theorem, First geometric form

Published on 22 Mar 2026 - 17:20

252

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The extension of functionals

Published on 25 Mar 2026 - 6:18

164

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Finitely Additive Homogeneous Translation Invariant Measure on $\mathcal{P}(\mathbb{R})$

Published on 25 Mar 2026 - 6:21

76

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Hahn-Banach needed to show equality?

Published on 25 Mar 2026 - 6:24

663

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If the dual of a topological vector space separates points, does it separate a point and a closed subspace?

Published on 25 Mar 2026 - 6:21

List Question

Proving that $\exists f \in X^*$ : $f(x) = \|x\|^2$ and $\|f\| = \|x\|$

Showing that $\exists f \in X^*$ : $\|f\| = \frac{1}{d(x_0,Y)}, \; f(x_0) = 1$ and $f(y) = 0$.

Show that $x_0 \in \overline{\langle M \rangle } $ if and only if $f(x_0) = 0, \; \forall f \in X^* : f|_M = 0$.

Easy way to extend continous functional

How to prove that continuous convex functional on normed vector space must be lower bounded by some continuous affine functional?

(Hahn-Banach) Is a subadditive and positively homogeneous function continuous at $0$?

An "open-strict" Version of Hahn Banach Separation Theorem?

are linear functionals on C[0, 1] bounded and thus continuous

Is a Hahn-Banach extension always continuous?

Corollary of the Hahn Banach theorem

Hahn Banach Theorem, First geometric form

The extension of functionals

Finitely Additive Homogeneous Translation Invariant Measure on $\mathcal{P}(\mathbb{R})$

Hahn-Banach needed to show equality?

If the dual of a topological vector space separates points, does it separate a point and a closed subspace?

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