Question

Prove that the $C^1([a,b],\mathbb R)$ together with the $C^1$-norm $\| \cdot \|$ is a Banach space

score 42 · Answer 1 · 2019-10-26 19:58:18

42

Views

Prove that the $C^1([a,b],\mathbb R)$ together with the $C^1$-norm $\| \cdot \|$ is a Banach space

Published on 26 Oct 2019 - 19:58

score 615 · Answer 2 · 2019-10-26 21:23:14

615

Views

$c$ and $c_0$ are not isometrically isomorphic

Published on 26 Oct 2019 - 21:23

score 60 · Answer 3 · 2019-10-26 22:47:29

60

Views

Proving a result of a function on $L^1[-1,1]$

Published on 26 Oct 2019 - 22:47

score 325 · Answer 4 · 2019-10-27 11:04:42

325

Views

Prove for any normed space finite dimensional is a Banach Space.

Published on 27 Oct 2019 - 11:04

score 104 · Answer 5 · 2019-10-27 12:24:22

104

Views

Prove that there is no function $g\in L^1[-1,1]$ such that $f(\phi)=\int_{-1}^1\phi g\,dx$ for all $\phi\in C[-1,1]$

Published on 27 Oct 2019 - 12:24

score 308 · Answer 6 · 2026-03-27 14:55:15

308

Views

Norms and convergence on direct product of Banach spaces

Published on 27 Mar 2026 - 14:55

score 26 · Answer 7 · 2019-10-27 21:17:54

26

Views

condition for an element to be limit of finite convex combination

Published on 27 Oct 2019 - 21:17

score 81 · Answer 8 · 2019-10-27 22:31:31

81

Views

Application of Banach-Steinhaus to prove a sequence is bounded

Published on 27 Oct 2019 - 22:31

score 127 · Answer 9 · 2019-10-29 11:23:13

127

Views

unilateral shift operator on $l^1(\mathbb{N})$

Published on 29 Oct 2019 - 11:23

score 100 · Answer 10 · 2026-03-27 22:16:27

100

Views

Homeomorphism between a piece of sphere and a convex set on a Banach space.

Published on 27 Mar 2026 - 22:16

score 165 · Answer 11 · 2026-03-30 06:31:23

165

Views

Operators unitarily equivalent to unilaterial shift on $\bigoplus_{k = -\infty}^{\infty} H_k$

Published on 30 Mar 2026 - 6:31

score 100 · Answer 12 · 2019-10-30 21:10:57

100

Views

Is $\mathcal C^1([a,b],\mathbb R)$ endowed with the $C^1$-norm a Hilbert space?

Published on 30 Oct 2019 - 21:10

score 122 · Answer 13 · 2019-10-31 09:12:34

122

Views

Proving that the Lebesgue space $L^1$ is complete using absolute convergence of series

Published on 31 Oct 2019 - 9:12

score 264 · Answer 14 · 2026-03-26 06:27:59

264

Views

Completeness of continuous $L^2$-martingales

Published on 26 Mar 2026 - 6:27

score 220 · Answer 15 · 2026-03-25 19:10:49

220

Views

The Etymology of the Term "Nuclear Operators"

Published on 25 Mar 2026 - 19:10

List Question

Prove that the $C^1([a,b],\mathbb R)$ together with the $C^1$-norm $\| \cdot \|$ is a Banach space

$c$ and $c_0$ are not isometrically isomorphic

Proving a result of a function on $L^1[-1,1]$

Prove for any normed space finite dimensional is a Banach Space.

Prove that there is no function $g\in L^1[-1,1]$ such that $f(\phi)=\int_{-1}^1\phi g\,dx$ for all $\phi\in C[-1,1]$

Norms and convergence on direct product of Banach spaces

condition for an element to be limit of finite convex combination

Application of Banach-Steinhaus to prove a sequence is bounded

unilateral shift operator on $l^1(\mathbb{N})$

Homeomorphism between a piece of sphere and a convex set on a Banach space.

Operators unitarily equivalent to unilaterial shift on $\bigoplus_{k = -\infty}^{\infty} H_k$

Is $\mathcal C^1([a,b],\mathbb R)$ endowed with the $C^1$-norm a Hilbert space?

Proving that the Lebesgue space $L^1$ is complete using absolute convergence of series

Completeness of continuous $L^2$-martingales

The Etymology of the Term "Nuclear Operators"

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