List questions from normed-spaces

Published on 15 Dec 2019 - 8:48

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Prove that two norms are equivalents.

Published on 06 Apr 2026 - 6:29

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Compute $\|x\|=\max_{1 \leq i_1 \leq \dots \leq i_r \leq n} |x_{i_1}| + \cdots + |x_{i_r}|$ by optimization?

Published on 04 Apr 2026 - 5:12

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Prove that the norm $||T_n - T|| = 1$ in $l^2$

Published on 15 Dec 2019 - 22:12

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A question about a family of seminorms inducing topology

Published on 16 Dec 2019 - 13:11

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What is the continuous spectrum of this linear operator?

Published on 08 Apr 2026 - 1:18

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Show that functional $f(x)$ is unbounded and norm $\|A\|=\infty$

Published on 06 Apr 2026 - 7:15

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Are Banach norms Fréchet differentiable?

Published on 25 Mar 2026 - 18:24

137

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Does the order preserve in different norm spaces?

Published on 17 Dec 2019 - 20:35

269

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Are strictly convex Banach norms Fréchet differentiable?

Published on 25 Mar 2026 - 18:31

166

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Folland's "equivalent" product norms

Published on 18 Dec 2019 - 11:53

33

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Proof $U_\epsilon (x) \cap U_\epsilon(y) \neq 0 \Leftrightarrow \Vert x-y\Vert < 2\epsilon$

Published on 18 Dec 2019 - 15:17

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Proof $\Vert x\Vert_\infty \leq \Vert x \Vert \leq \sqrt{n}\Vert x\Vert_\infty$

Published on 18 Dec 2019 - 15:36

66

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Are all FD-spaces strictly convex?

Published on 25 Mar 2026 - 18:24

42

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How to obtain the distance (dissimilarity) between two vectors?

Published on 19 Dec 2019 - 12:35

List Question

Matrix in norm subscript notation

Prove that two norms are equivalents.

Compute $\|x\|=\max_{1 \leq i_1 \leq \dots \leq i_r \leq n} |x_{i_1}| + \cdots + |x_{i_r}|$ by optimization?

Prove that the norm $||T_n - T|| = 1$ in $l^2$

A question about a family of seminorms inducing topology

What is the continuous spectrum of this linear operator?

Show that functional $f(x)$ is unbounded and norm $\|A\|=\infty$

Are Banach norms Fréchet differentiable?

Does the order preserve in different norm spaces?

Are strictly convex Banach norms Fréchet differentiable?

Folland's "equivalent" product norms

Proof $U_\epsilon (x) \cap U_\epsilon(y) \neq 0 \Leftrightarrow \Vert x-y\Vert < 2\epsilon$

Proof $\Vert x\Vert_\infty \leq \Vert x \Vert \leq \sqrt{n}\Vert x\Vert_\infty$

Are all FD-spaces strictly convex?

How to obtain the distance (dissimilarity) between two vectors?

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