Question

Does $\Vert T\Vert=\max\{\Vert T(x)\Vert/\Vert x\Vert:x\neq 0\}$?

score 305 · Answer 1 · 2018-08-28 23:30:49

305

Views

Does $\Vert T\Vert=\max\{\Vert T(x)\Vert/\Vert x\Vert:x\neq 0\}$?

Published on 28 Aug 2018 - 23:30

score 642 · Answer 2 · 2018-08-28 23:54:33

642

Views

How to prove that something is $\textit{not}$ an inner-product space

Published on 28 Aug 2018 - 23:54

score 627 · Answer 3 · 2018-08-29 13:24:47

627

Views

Is the distance between two elements of a normed vector space at least the distance between their projections on the unit ball?

Published on 29 Aug 2018 - 13:24

score 115 · Answer 4 · 2018-08-30 01:23:40

115

Views

If $\langle f(t,y),y\rangle\leq \alpha(t)\left(1+\Vert y \Vert^2\right),\forall\, t\geq 0,\,y\in\Bbb{R}^n$ then $x'(t)$ has a global solution

Published on 30 Aug 2018 - 1:23

score 59 · Answer 5 · 2026-03-27 05:05:58

59

Views

A Soft question about writing one theorem in Introduction.

Published on 27 Mar 2026 - 5:05

score 6.8k · Answer 6 · 2026-03-27 14:53:41

6.8k

Views

Proof for: the norm of the product between two vectors is equal to the product of their norms

Published on 27 Mar 2026 - 14:53

score 49 · Answer 7 · 2026-03-25 08:09:24

49

Views

Existence of 1-complemented hyperplanes in finite dimensional normed spaces

Published on 25 Mar 2026 - 8:09

score 29 · Answer 8 · 2026-02-23 06:38:40

29

Views

Particular sequence in $L^2[0,1]$ that fades at $\infty$ in $L^2$ norm and whose limit is not defined $\forall$ t

Published on 23 Feb 2026 - 6:38

score 47 · Answer 9 · 2018-08-30 16:35:30

47

Views

Equivalence on objective function of an optimization problem

Published on 30 Aug 2018 - 16:35

score 97 · Answer 10 · 2018-08-31 04:12:19

97

Views

Different notions of equivalence of norms

Published on 31 Aug 2018 - 4:12

score 243 · Answer 11 · 2018-08-31 13:13:53

243

Views

Composition of two linear continuous functions

Published on 31 Aug 2018 - 13:13

score 28 · Answer 12 · 2026-03-27 12:00:30

28

Views

Adding scaled number

Published on 27 Mar 2026 - 12:00

score 269 · Answer 13 · 2026-03-25 07:40:51

269

Views

Constructive proof of $\Vert x \Vert = 0 \Rightarrow x = {\mathbf0}$.

Published on 25 Mar 2026 - 7:40

score 206 · Answer 14 · 2026-03-26 19:02:54

206

Views

Is it true that $4$ distinct points in the plane form a rhombus if and only if the set of their distances contains exactly $2$ or $3$ elements?

Published on 26 Mar 2026 - 19:02

score 491 · Answer 15 · 2018-09-01 01:41:09

491

Views

Example of a metric on $\mathbb{R}^2$ that is not induced by any norm.

Published on 01 Sep 2018 - 1:41

List Question

Does $\Vert T\Vert=\max\{\Vert T(x)\Vert/\Vert x\Vert:x\neq 0\}$?

How to prove that something is $\textit{not}$ an inner-product space

Is the distance between two elements of a normed vector space at least the distance between their projections on the unit ball?

If $\langle f(t,y),y\rangle\leq \alpha(t)\left(1+\Vert y \Vert^2\right),\forall\, t\geq 0,\,y\in\Bbb{R}^n$ then $x'(t)$ has a global solution

A Soft question about writing one theorem in Introduction.

Proof for: the norm of the product between two vectors is equal to the product of their norms

Existence of 1-complemented hyperplanes in finite dimensional normed spaces

Particular sequence in $L^2[0,1]$ that fades at $\infty$ in $L^2$ norm and whose limit is not defined $\forall$ t

Equivalence on objective function of an optimization problem

Different notions of equivalence of norms

Composition of two linear continuous functions

Adding scaled number

Constructive proof of $\Vert x \Vert = 0 \Rightarrow x = {\mathbf0}$.

Is it true that $4$ distinct points in the plane form a rhombus if and only if the set of their distances contains exactly $2$ or $3$ elements?

Example of a metric on $\mathbb{R}^2$ that is not induced by any norm.

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