List questions from normed-spaces

Published on 16 Dec 2018 - 18:44

352

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Bidual Banach space

Published on 16 Dec 2018 - 20:08

173

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Operator norm $ ( \ell_2 \to \ell_1)$

Published on 29 Mar 2026 - 15:14

354

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Operator norm on Lebesgue integrable functions

Published on 28 Mar 2026 - 7:57

1.2k

Views

Weighted P-norm

Published on 29 Mar 2026 - 15:23

593

Views

Find an example of a random vector $X$ with its sub-gaussian norm much larger than any of its coordinates'.

Published on 27 Mar 2026 - 22:00

490

Views

Difference between a bounded linear map and a Lipschitz linear map

Published on 17 Dec 2018 - 8:22

851

Views

If $T:X\to Y$ is a continuous linear map at the origin, then $T$ is Lipschitz

Published on 17 Dec 2018 - 9:38

119

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

Published on 27 Mar 2026 - 17:49

56

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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 28 Mar 2026 - 9:08

172

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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 28 Mar 2026 - 0:50

919

Views

Proving that $\Vert T \Vert =\sup\limits_{\Vert x \Vert\leq 1}\Vert T x \Vert= \sup\limits_{\Vert x \Vert = 1}\Vert T x \Vert \cdots$

Published on 17 Dec 2018 - 21:15

172

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Is every normable topological vector space "inner productable"?

Published on 26 Mar 2026 - 6:20

24.1k

Views

$L^2$ norm of a matrix: Is this statement true?

Published on 30 Mar 2026 - 15:04

302

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Proving that $\Vert T \Vert =\sup\limits_{\Vert x \Vert\leq 1}\Vert T x \Vert$ defines a norm on $B(X,Y). $

Published on 18 Dec 2018 - 9:20

List Question

Adjoint operator definition

Bidual Banach space

Operator norm $ ( \ell_2 \to \ell_1)$

Operator norm on Lebesgue integrable functions

Weighted P-norm

Find an example of a random vector $X$ with its sub-gaussian norm much larger than any of its coordinates'.

Difference between a bounded linear map and a Lipschitz linear map

If $T:X\to Y$ is a continuous linear map at the origin, then $T$ is Lipschitz

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 $f(x_0) = 0, \; \forall f \in X^* : f|_M = 0$.

Proving that $\Vert T \Vert =\sup\limits_{\Vert x \Vert\leq 1}\Vert T x \Vert= \sup\limits_{\Vert x \Vert = 1}\Vert T x \Vert \cdots$

Is every normable topological vector space "inner productable"?

$L^2$ norm of a matrix: Is this statement true?

Proving that $\Vert T \Vert =\sup\limits_{\Vert x \Vert\leq 1}\Vert T x \Vert$ defines a norm on $B(X,Y). $

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