List questions from normed-spaces

Published on 11 Apr 2026 - 8:26

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Find a function that has a 1 or 2 norm but not an infinity norm.

Published on 16 Apr 2026 - 21:09

285

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Given a space, what is the inner product?

Published on 12 Apr 2026 - 16:12

50

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Find $E$ : $\| x \|_1 \le E \| x \|_2 $

Published on 12 Apr 2026 - 16:54

3.5k

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Proving that the space of bounded linear operators is complete

Published on 15 Apr 2026 - 3:35

226

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Find the value of $\alpha-\beta$ if $g(x,y)=\alpha x+\beta y$ is a Hahn-Banach extension of $f$

Published on 16 Apr 2026 - 6:13

245

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Does there exist any surjective continuous linear map $T:l^2 \to l^1$?

Published on 15 Apr 2026 - 3:41

190

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Is any multiplicative linear functional $ \Phi $ on $ C([a,b]) $ bounded?

Published on 12 Apr 2026 - 2:54

5.7k

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2-norm of a matrix

Published on 13 Apr 2026 - 23:57

567

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Can every separable Banach space be isometrically embedded in $l^2$ ? Or at least in $l^p$ for some $1\le p<\infty$?

Published on 15 Apr 2026 - 14:54

175

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Conditions on a matrix for a sequence to converge

Published on 10 Apr 2026 - 23:36

164

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Distance and norm in a linear subspace

Published on 16 Apr 2026 - 12:41

15.1k

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Proof for infinity matrix norm

Published on 10 Apr 2026 - 8:42

97

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Are $L_p$ spaces $L_p$-saturated?

Published on 11 Apr 2026 - 17:40

62

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Show that $ \Lambda:a\mapsto \Lambda_a $ defines a linear map from $ l^1(\mathbb{N}) $ to $ c^0(\mathbb{N})^* $

Published on 16 Apr 2026 - 15:35

List Question

Why we don't define the norm of operator $A$ as $\inf\limits_{||u||=1}||Au||$?

Find a function that has a 1 or 2 norm but not an infinity norm.

Given a space, what is the inner product?

Find $E$ : $\| x \|_1 \le E \| x \|_2 $

Proving that the space of bounded linear operators is complete

Find the value of $\alpha-\beta$ if $g(x,y)=\alpha x+\beta y$ is a Hahn-Banach extension of $f$

Does there exist any surjective continuous linear map $T:l^2 \to l^1$?

Is any multiplicative linear functional $ \Phi $ on $ C([a,b]) $ bounded?

2-norm of a matrix

Can every separable Banach space be isometrically embedded in $l^2$ ? Or at least in $l^p$ for some $1\le p<\infty$?

Conditions on a matrix for a sequence to converge

Distance and norm in a linear subspace

Proof for infinity matrix norm

Are $L_p$ spaces $L_p$-saturated?

Show that $ \Lambda:a\mapsto \Lambda_a $ defines a linear map from $ l^1(\mathbb{N}) $ to $ c^0(\mathbb{N})^* $

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