Question

Let $E$ a normed vector space and $L \neq E$ a vector subspace of $E$. Can $L$ contain any open ball of $E$?

score 67 · Answer 1 · 2020-07-26 01:49:31

67

Views

Let $E$ a normed vector space and $L \neq E$ a vector subspace of $E$. Can $L$ contain any open ball of $E$?

Published on 26 Jul 2020 - 1:49

score 30 · Answer 2 · 2026-03-30 07:09:22

30

Views

If $L_A:(\mathbb{R}^2, \| \cdot \|_p) \to (\mathbb{R}^3, \| \cdot \|_p )$ is an isometry, is set of columns of $A$ orthonormal?

Published on 30 Mar 2026 - 7:09

score 70 · Answer 3 · 2026-04-12 21:39:31

70

Views

Let T be a linear operator from normed spaces X to Y if $m\|x\|\leq \|T(x)\|$ for $m>0$ then $T^{-1}$ exists and continuous.

Published on 12 Apr 2026 - 21:39

score 216 · Answer 4 · 2020-07-26 16:38:55

216

Views

If $(X,| \cdot|)$ is isometrically isomorphic with $(X,\|\cdot \|)$ is it always true that the norms are equivalent??

Published on 26 Jul 2020 - 16:38

score 34 · Answer 5 · 2020-07-27 07:57:15

34

Views

evaluate the limit of $\frac {x}{|x|^s}$ as $s<1$ and $x$ goes to $0$

Published on 27 Jul 2020 - 7:57

score 1.4k · Answer 6 · 2026-04-12 18:44:25

1.4k

Views

Are balls around a point always symmetric about the axes?

Published on 12 Apr 2026 - 18:44

score 74 · Answer 7 · 2026-04-10 21:50:58

74

Views

Finding the upper bound of a linear functional

Published on 10 Apr 2026 - 21:50

score 244 · Answer 8 · 2026-03-25 11:00:06

244

Views

Frobenius norm: completing squares and minimizing

Published on 25 Mar 2026 - 11:00

score 415 · Answer 9 · 2026-04-10 13:41:57

415

Views

How to prove that $|f|\leqslant\|f\|_\infty$ almost everywhere?

Published on 10 Apr 2026 - 13:41

score 47 · Answer 10 · 2026-04-13 15:03:48

47

Views

Connection between linear mappings and continous mappings

Published on 13 Apr 2026 - 15:03

score 78 · Answer 11 · 2026-04-13 07:49:26

78

Views

One-sided limit of q norm on $[0,1]$

Published on 13 Apr 2026 - 7:49

score 42 · Answer 12 · 2020-07-30 08:39:16

42

Views

Let continuous $T:X\to Y$ with $(X,||.||)$ and $(Y,||.||')$ normed spaces.Is it always true that $T(Bx)=By$?

Published on 30 Jul 2020 - 8:39

score 111 · Answer 13 · 2026-04-08 00:16:08

111

Views

Show that in a Hilbert space, $||x+\alpha y|| \ge ||x|| \,\forall\,\alpha\in\mathbb{C}\implies (x,y)=0$

Published on 08 Apr 2026 - 0:16

score 366 · Answer 14 · 2026-04-08 19:05:49

366

Views

Is $AC[a,b]$ closed in $(BV[a,b],TV)$?

Published on 08 Apr 2026 - 19:05

score 194 · Answer 15 · 2026-04-13 06:03:55

194

Views

Projections satisfying $\| Px-Qx \| <\|x \|$ for nonzero $x$?

Published on 13 Apr 2026 - 6:03

List Question

Let $E$ a normed vector space and $L \neq E$ a vector subspace of $E$. Can $L$ contain any open ball of $E$?

If $L_A:(\mathbb{R}^2, \| \cdot \|_p) \to (\mathbb{R}^3, \| \cdot \|_p )$ is an isometry, is set of columns of $A$ orthonormal?

Let T be a linear operator from normed spaces X to Y if $m\|x\|\leq \|T(x)\|$ for $m>0$ then $T^{-1}$ exists and continuous.

If $(X,| \cdot|)$ is isometrically isomorphic with $(X,\|\cdot \|)$ is it always true that the norms are equivalent??

evaluate the limit of $\frac {x}{|x|^s}$ as $s<1$ and $x$ goes to $0$

Are balls around a point always symmetric about the axes?

Finding the upper bound of a linear functional

Frobenius norm: completing squares and minimizing

How to prove that $|f|\leqslant\|f\|_\infty$ almost everywhere?

Connection between linear mappings and continous mappings

One-sided limit of q norm on $[0,1]$

Let continuous $T:X\to Y$ with $(X,||.||)$ and $(Y,||.||')$ normed spaces.Is it always true that $T(Bx)=By$?

Show that in a Hilbert space, $||x+\alpha y|| \ge ||x|| \,\forall\,\alpha\in\mathbb{C}\implies (x,y)=0$

Is $AC[a,b]$ closed in $(BV[a,b],TV)$?

Projections satisfying $\| Px-Qx \| <\|x \|$ for nonzero $x$?

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