Question

Prove that $||f|| :=\int^1_0 |f(t)|dt$ is the norm of the linear space $C[0,1]$ of continuous functions of the interval $[0,1]$.

score 118 · Answer 1 · 2023-12-13 10:41:42

118

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Prove that $||f|| :=\int^1_0 |f(t)|dt$ is the norm of the linear space $C[0,1]$ of continuous functions of the interval $[0,1]$.

Published on 13 Dec 2023 - 10:41

score 36 · Answer 2 · 2026-04-08 02:46:26

36

Views

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score 51 · Answer 3 · 2026-04-08 00:00:46

51

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score 86 · Answer 4 · 2023-12-16 14:29:55

86

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Calculating operator norm of operator $(Ax)(k) = \int_{0}^{1} x(t)\operatorname{arcctg}\left((-1)^kt\right) \,\mathrm{d}t$

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score 81 · Answer 5 · 2026-03-25 09:50:47

81

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32

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score 66 · Answer 7 · 2023-12-17 12:40:24

66

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score 38 · Answer 8 · 2026-04-07 16:54:02

38

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score 79 · Answer 9 · 2023-12-19 10:14:04

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score 226 · Answer 10 · 2026-03-26 12:52:46

226

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score 38 · Answer 11 · 2023-12-25 12:02:22

38

Views

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score 111 · Answer 12 · 2023-12-25 14:45:41

111

Views

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score 70 · Answer 13 · 2023-12-26 16:02:44

70

Views

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score 59 · Answer 14 · 2023-12-26 19:05:56

59

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score 67 · Answer 15 · 2023-12-30 17:28:32

67

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List Question

Prove that $||f|| :=\int^1_0 |f(t)|dt$ is the norm of the linear space $C[0,1]$ of continuous functions of the interval $[0,1]$.

A question on equivalent norms on Sobolev spaces

Equivalent bases in Banach spaces definition

Calculating operator norm of operator $(Ax)(k) = \int_{0}^{1} x(t)\operatorname{arcctg}\left((-1)^kt\right) \,\mathrm{d}t$

Gauge integral on infinite-dimensional Banach space and differentiability

Commuting Bounded linear projections

Show that linear map on Banach space is bounded

How to prove the completeness of $L_2(\Omega)$

Proof of uniform boundedness property in Folland

Definition of weak convergence

Minimizing vector for a closed set in $L^3$

Prove that $T$ is continuous if and only if $N_T=\{0\}$

Showing that $i:\ell^1 \to S_C$ has dense range.

Hyperplane in a reflexive Banach space achieves its minimum norm

Split monomorphism and split epimorphisms of Banach spaces

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