List questions from normed-spaces

41

Views

Let $a, b$, be positives and $a \leq b$. For which $p$ the function $\frac{1} {x^a+x^b}$ is $L_p(0,+\infty)$?

Published on 29 Mar 2026 - 16:29

247

Views

How to show that if $x^T x = 0$, then $x=0$ for any column vector $x$?

Published on 08 Mar 2019 - 18:08

112

Views

$c_0(N)$ is not dense in $c(N)$ for any norm.

Published on 09 Mar 2019 - 16:07

127

Views

The third dual can be "decomposed" with the dual and his annihilator

Published on 28 Mar 2026 - 16:13

55

Views

Show that the function $f$ defined in $l_1$ by $f(x)=\Big(\Big(\sum|x_i|\Big)^2+\sum\frac{1}{2^i}|x_i|^2\Big)^{1/2}$ is a norm equivalent in $l_1$

Published on 09 Mar 2019 - 18:08

413

Views

Understanding the proof to continuity of norms in normed spaces

Published on 10 Mar 2019 - 6:02

180

Views

Proving an inequality based on condition number.

Published on 25 Mar 2026 - 3:34

122

Views

Rudin Functional analysis, theorem 4.12 corollary (b)

Published on 25 Mar 2026 - 12:33

226

Views

Triangle Inequality for p-norm on nxn real matrices

Published on 12 Mar 2019 - 2:57

40

Views

$\| X'(t) \| = (\| X(t) \|)'$

Published on 12 Mar 2019 - 8:15

602

Views

Norms on fields

Published on 26 Mar 2026 - 17:52

273

Views

What are the definitions of the Matrix norms?

Published on 25 Mar 2026 - 6:05

636

Views

Spectral norm of matrices with complex eigenvalues

Published on 25 Mar 2026 - 7:32

59

Views

Problem with norms over $\mathbb{R}^2$

Published on 13 Mar 2019 - 13:18

328

Views

Show that graph of operator with adjoint operator is closed

Published on 26 Mar 2026 - 13:57

List Question

Let $a, b$, be positives and $a \leq b$. For which $p$ the function $\frac{1} {x^a+x^b}$ is $L_p(0,+\infty)$?

How to show that if $x^T x = 0$, then $x=0$ for any column vector $x$?

$c_0(N)$ is not dense in $c(N)$ for any norm.

The third dual can be "decomposed" with the dual and his annihilator

Show that the function $f$ defined in $l_1$ by $f(x)=\Big(\Big(\sum|x_i|\Big)^2+\sum\frac{1}{2^i}|x_i|^2\Big)^{1/2}$ is a norm equivalent in $l_1$

Understanding the proof to continuity of norms in normed spaces

Proving an inequality based on condition number.

Rudin Functional analysis, theorem 4.12 corollary (b)

Triangle Inequality for p-norm on nxn real matrices

$\| X'(t) \| = (\| X(t) \|)'$

Norms on fields

What are the definitions of the Matrix norms?

Spectral norm of matrices with complex eigenvalues

Problem with norms over $\mathbb{R}^2$

Show that graph of operator with adjoint operator is closed

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