Question

Is a bounded Operator $T\colon X\to Y$ which satisfies $\beta\lVert x\rVert\leq\lVert Tx\rVert$ for some $\beta > 0$ and all $x\in X$ an isometry?

score 57 · Answer 1 · 2021-11-10 23:48:52

57

Views

Is a bounded Operator $T\colon X\to Y$ which satisfies $\beta\lVert x\rVert\leq\lVert Tx\rVert$ for some $\beta > 0$ and all $x\in X$ an isometry?

Published on 10 Nov 2021 - 23:48

score 346 · Answer 2 · 2026-02-23 13:40:31

346

Views

Defining a rigid sphere

Published on 23 Feb 2026 - 13:40

score 41 · Answer 3 · 2021-11-23 05:30:23

41

Views

Isometric deformation of semisphere in $\mathbb{R^3}$

Published on 23 Nov 2021 - 5:30

score 139 · Answer 4 · 2021-11-26 05:29:42

139

Views

Is the symmetry group of a compact subset of $\mathbb{R}^n$ closed?

Published on 26 Nov 2021 - 5:29

score 377 · Answer 5 · 2026-03-26 16:05:21

377

Views

Quasi-isometry of finitely generated group

Published on 26 Mar 2026 - 16:05

score 622 · Answer 6 · 2026-03-29 08:35:21

622

Views

Explicitly representing an isometry as a composition of circle inversions

Published on 29 Mar 2026 - 8:35

score 21 · Answer 7 · 2026-03-25 19:04:09

21

Views

How to quasify a proposition that holds for trees to general hyperbolic spaces?

Published on 25 Mar 2026 - 19:04

score 49 · Answer 8 · 2026-03-31 05:41:36

49

Views

Isometry of $(V\times W)^$ with $V^\times W^*$

Published on 31 Mar 2026 - 5:41

score 137 · Answer 9 · 2026-03-30 12:25:43

137

Views

Metric space isometries and integration by substitution

Published on 30 Mar 2026 - 12:25

score 113 · Answer 10 · 2026-03-31 05:42:44

113

Views

Identification of $\ell_1^n$ $(\ell_\infty^n)$ with $\ell_\infty^{n^}$ $(\ell_1^{n^})$.

Published on 31 Mar 2026 - 5:42

score 62 · Answer 11 · 2021-12-15 20:18:07

62

Views

Metric induced on linear group orbit is Riemannian homogeneous

Published on 15 Dec 2021 - 20:18

score 95 · Answer 12 · 2026-03-30 05:32:21

95

Views

Intuition for no isometric embedding of round projective plane into $\mathbb{R}^4 $

Published on 30 Mar 2026 - 5:32

score 75 · Answer 13 · 2021-12-19 14:16:55

75

Views

Show that $T$ is isometric and not surjective. Proof validation.

Published on 19 Dec 2021 - 14:16

score 457 · Answer 14 · 2021-12-23 07:45:07

457

Views

There exists a a metric space such that its group of isometries is isomorphic to $\mathbb{Z}$.

Published on 23 Dec 2021 - 7:45

score 49 · Answer 15 · 2021-12-26 21:54:50

49

Views

Prove that the following application between $M_{n×n}(\Bbb R)$ and $M_{n^2×n^2}(\Bbb R)$ is an isometry such that $\det φ(X)≠ 0$ whether $\det X≠ 0$

Published on 26 Dec 2021 - 21:54

List Question

Is a bounded Operator $T\colon X\to Y$ which satisfies $\beta\lVert x\rVert\leq\lVert Tx\rVert$ for some $\beta > 0$ and all $x\in X$ an isometry?

Defining a rigid sphere

Isometric deformation of semisphere in $\mathbb{R^3}$

Is the symmetry group of a compact subset of $\mathbb{R}^n$ closed?

Quasi-isometry of finitely generated group

Explicitly representing an isometry as a composition of circle inversions

How to quasify a proposition that holds for trees to general hyperbolic spaces?

Isometry of $(V\times W)^$ with $V^\times W^*$

Metric space isometries and integration by substitution

Identification of $\ell_1^n$ $(\ell_\infty^n)$ with $\ell_\infty^{n^}$ $(\ell_1^{n^})$.

Metric induced on linear group orbit is Riemannian homogeneous

Intuition for no isometric embedding of round projective plane into $\mathbb{R}^4 $

Show that $T$ is isometric and not surjective. Proof validation.

There exists a a metric space such that its group of isometries is isomorphic to $\mathbb{Z}$.

Prove that the following application between $M_{n×n}(\Bbb R)$ and $M_{n^2×n^2}(\Bbb R)$ is an isometry such that $\det φ(X)≠ 0$ whether $\det X≠ 0$

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