Question

Proving that every norm is continuous with respect to $\lVert\cdot\rVert_\infty$

score 221 · Answer 1 · 2026-04-14 11:01:56

221

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Proving that every norm is continuous with respect to $\lVert\cdot\rVert_\infty$

Published on 14 Apr 2026 - 11:01

score 668 · Answer 2 · 2026-04-16 20:49:37

668

Views

Distance of element of normed space to finite dimensional subspace is realised by element of subspace

Published on 16 Apr 2026 - 20:49

score 1.3k · Answer 3 · 2026-04-14 10:00:23

1.3k

Views

Norm of diagonal and orthogonal matrix

Published on 14 Apr 2026 - 10:00

score 2k · Answer 4 · 2026-04-13 18:07:22

2k

Views

An infinite dimensional normed vector space is closed and bounded, but not compact

Published on 13 Apr 2026 - 18:07

score 36 · Answer 5 · 2026-04-14 03:02:46

36

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Norms on vector spaces

Published on 14 Apr 2026 - 3:02

score 103 · Answer 6 · 2026-04-16 01:31:33

103

Views

For all subspaces $B$ of normed spaces $A$ there exista $a\in A$ s.t. $||a||=1$ and $d(a,B)=\inf_{b\in B}||a-b||>1-\epsilon$

Published on 16 Apr 2026 - 1:31

score 888 · Answer 7 · 2026-04-15 18:40:41

888

Views

Example of minimal norm elements in a convex subset

Published on 15 Apr 2026 - 18:40

score 154 · Answer 8 · 2026-04-16 23:00:21

154

Views

Space of measurable functions not normable

Published on 16 Apr 2026 - 23:00

score 344 · Answer 9 · 2026-04-15 05:59:59

344

Views

Show that $\| f(x) - f(y) \| \leq 2 \| x - y \| $

Published on 15 Apr 2026 - 5:59

score 1.3k · Answer 10 · 2026-04-14 19:55:46

1.3k

Views

Lipschitz continuity and $l^1$ norm

Published on 14 Apr 2026 - 19:55

score 96 · Answer 11 · 2026-04-13 21:57:38

96

Views

Show metrics induced by ${\parallel \cdot \parallel}_1 ,{\parallel \cdot \parallel}_2, {\parallel \cdot \parallel}_{\infty}$ are equivalent

Published on 13 Apr 2026 - 21:57

score 66 · Answer 12 · 2026-04-15 04:23:02

If $T:V\to W$ is linear, prove that $\langle x, y \rangle = \langle T(x), T(y)\rangle$ defines an inner product on $V$ iff $T$ is one-to-one.

score 2.9k · Answer 13 · 2026-04-10 11:21:16

2.9k

Views

Subordinate matrix norm of $1$-norm

Published on 10 Apr 2026 - 11:21

score 1k · Answer 14 · 2026-04-12 17:00:02

1k

Views

Operator norm of a functional

Published on 12 Apr 2026 - 17:00

score 181 · Answer 15 · 2026-04-09 02:01:25

181

Views

Operator norm in C*-algebra

Published on 09 Apr 2026 - 2:01

List Question

Proving that every norm is continuous with respect to $\lVert\cdot\rVert_\infty$

Distance of element of normed space to finite dimensional subspace is realised by element of subspace

Norm of diagonal and orthogonal matrix

An infinite dimensional normed vector space is closed and bounded, but not compact

Norms on vector spaces

For all subspaces $B$ of normed spaces $A$ there exista $a\in A$ s.t. $||a||=1$ and $d(a,B)=\inf_{b\in B}||a-b||>1-\epsilon$

Example of minimal norm elements in a convex subset

Space of measurable functions not normable

Show that $\| f(x) - f(y) \| \leq 2 \| x - y \| $

Lipschitz continuity and $l^1$ norm

Show metrics induced by ${\parallel \cdot \parallel}_1 ,{\parallel \cdot \parallel}_2, {\parallel \cdot \parallel}_{\infty}$ are equivalent

If $T:V\to W$ is linear, prove that $\langle x, y \rangle = \langle T(x), T(y)\rangle$ defines an inner product on $V$ iff $T$ is one-to-one.

Subordinate matrix norm of $1$-norm

Operator norm of a functional

Operator norm in C*-algebra

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