List questions from normed-spaces

Published on 17 Oct 2019 - 13:22

58

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For $\Bbb{R}^m$ metrics $d_1(v,w)=\sum|v_i-w_i|$, $d_2(v,w)=\sqrt{\sum(v_i-w_i)^2}$, why does checking $w=0$ suffice to show $d_1(v,w)\leq d_2(v,w)$?

Published on 17 Oct 2019 - 22:01

61

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about a lemma for the proof of submultiplicativity of matrix norm

Published on 18 Oct 2019 - 1:37

115

Views

How does one calculate the norm $||f_n||_{\infty} = sup_{x \in [0,1]} |f_n(x)|$?

Published on 29 Mar 2026 - 5:34

161

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Prove two linear functions cannot both be bounded.

Published on 18 Oct 2019 - 6:17

115

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Proving the equality $\int |f|^p = \int_0^\infty pt^{p-1} \mu(\{x: |f(x)|\geq t\})) dt$ for $\sigma$-finite measure

Published on 03 Apr 2026 - 1:04

26

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Is $\text{ball}_{R}(X^{\ast})\cap\bigcap_{i\in I}\{x^{\ast}\in X^{\ast} | \ |x^{\ast}(x_i)|\leq r_i\}$ norm (or weak*) connected?

Published on 31 Mar 2026 - 16:57

32

Views

Prove that $f$ belongs to $B(X,\mathbb C)$ and evaluate $\Vert f \Vert$.

Published on 29 Mar 2026 - 12:32

78

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Gilbert Strang Frobenius question

Published on 18 Oct 2019 - 20:59

52

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Show that $\| \cdot \|^2: X \to \mathbb R$ is convex

Published on 19 Oct 2019 - 5:43

64

Views

Triangle inequality for complex function

Published on 19 Oct 2019 - 17:46

105

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$N_1N_2N_3=\{x\in F^{\times}| x^2\in N\}$

Published on 06 Apr 2026 - 0:54

105

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a affine hyperplane in normed space

Published on 26 Mar 2026 - 15:16

410

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definition of affine normed space

Published on 26 Mar 2026 - 15:17

21

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How to chose the kernel in order to minimize the operator norm?

Published on 21 Oct 2019 - 15:57

List Question

Concrete counterexample for norms on quotient spaces

For $\Bbb{R}^m$ metrics $d_1(v,w)=\sum|v_i-w_i|$, $d_2(v,w)=\sqrt{\sum(v_i-w_i)^2}$, why does checking $w=0$ suffice to show $d_1(v,w)\leq d_2(v,w)$?

about a lemma for the proof of submultiplicativity of matrix norm

How does one calculate the norm $||f_n||_{\infty} = sup_{x \in [0,1]} |f_n(x)|$?

Prove two linear functions cannot both be bounded.

Proving the equality $\int |f|^p = \int_0^\infty pt^{p-1} \mu(\{x: |f(x)|\geq t\})) dt$ for $\sigma$-finite measure

Is $\text{ball}_{R}(X^{\ast})\cap\bigcap_{i\in I}\{x^{\ast}\in X^{\ast} | \ |x^{\ast}(x_i)|\leq r_i\}$ norm (or weak*) connected?

Prove that $f$ belongs to $B(X,\mathbb C)$ and evaluate $\Vert f \Vert$.

Gilbert Strang Frobenius question

Show that $\| \cdot \|^2: X \to \mathbb R$ is convex

Triangle inequality for complex function

$N_1N_2N_3=\{x\in F^{\times}| x^2\in N\}$

a affine hyperplane in normed space

definition of affine normed space

How to chose the kernel in order to minimize the operator norm?

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