Banach space and normed space [closed]
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Can someone please help me solve this statement?
Consider the vector space $C^1 [0, 1]$ of the differentiable functions with continuous derivative in the interval $[0, 1]$.
For $fin C^1[0,1]$, let $N (f):= max{|f'(x)| : x ∈ [0, 1]}$.
i) Check whether $N$ is a norm on $C^1[0, 1]$.
ii) If not, identify, if any, a subspace ${0} ≠ X ⊆ C^1 ([0, 1])$ on which $N$ is a norm.
As for my thoughts? I am unable to apply the properties of the norm by proving so that N is not a norm in $C¹ [(0,1)]$ then indicate a subspace ${0} ≠ X ⊆ C¹ ([0, 1])$ in which $N$ is a norm.
functional-analysis banach-spaces
edited Dec 6 '18 at 18:07
user334732
4,26311240
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
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closed as off-topic by GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138 Dec 6 '18 at 2:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Can someone please help me solve this statement?
Consider the vector space $C^1 [0, 1]$ of the differentiable functions with continuous derivative in the interval $[0, 1]$.
For $fin C^1[0,1]$, let $N (f):= max{|f'(x)| : x ∈ [0, 1]}$.
i) Check whether $N$ is a norm on $C^1[0, 1]$.
ii) If not, identify, if any, a subspace ${0} ≠ X ⊆ C^1 ([0, 1])$ on which $N$ is a norm.
As for my thoughts? I am unable to apply the properties of the norm by proving so that N is not a norm in $C¹ [(0,1)]$ then indicate a subspace ${0} ≠ X ⊆ C¹ ([0, 1])$ in which $N$ is a norm.
functional-analysis banach-spaces
edited Dec 6 '18 at 18:07
user334732
4,26311240
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
$endgroup$
closed as off-topic by GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138 Dec 6 '18 at 2:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
3
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Hi, what are your thoughts on the given problem ?
$endgroup$
– Rebellos
Dec 5 '18 at 21:05
$begingroup$
Hi, I am unable to apply the properties of the norm by proving so that N is not a norm in C¹ [(0,1)] then indicate a subspace {0} ≠ X ⊆ C¹ ([0, 1]) in which N is a norm.
$endgroup$
– Paulo Marcos Ribeiro
Dec 6 '18 at 10:25
$begingroup$
Hi Paulo and welcome to MSE. 1. Your thoughts on the problem, which you have added in a comment, you should add to the question itself, so the question fits site policies. 2. If you had pinged Rebellos by typing an "@" followed by his username he would have seen your comment.
$endgroup$
– user334732
Dec 6 '18 at 18:06
$begingroup$
And 3. you can use mathjax in comments. math.meta.stackexchange.com/questions/5020
$endgroup$
– user334732
Dec 6 '18 at 18:08
add a comment |
$begingroup$
Can someone please help me solve this statement?
Consider the vector space $C^1 [0, 1]$ of the differentiable functions with continuous derivative in the interval $[0, 1]$.
For $fin C^1[0,1]$, let $N (f):= max{|f'(x)| : x ∈ [0, 1]}$.
i) Check whether $N$ is a norm on $C^1[0, 1]$.
ii) If not, identify, if any, a subspace ${0} ≠ X ⊆ C^1 ([0, 1])$ on which $N$ is a norm.
As for my thoughts? I am unable to apply the properties of the norm by proving so that N is not a norm in $C¹ [(0,1)]$ then indicate a subspace ${0} ≠ X ⊆ C¹ ([0, 1])$ in which $N$ is a norm.
functional-analysis banach-spaces
edited Dec 6 '18 at 18:07
user334732
4,26311240
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
$endgroup$
Can someone please help me solve this statement?
Consider the vector space $C^1 [0, 1]$ of the differentiable functions with continuous derivative in the interval $[0, 1]$.
For $fin C^1[0,1]$, let $N (f):= max{|f'(x)| : x ∈ [0, 1]}$.
i) Check whether $N$ is a norm on $C^1[0, 1]$.
ii) If not, identify, if any, a subspace ${0} ≠ X ⊆ C^1 ([0, 1])$ on which $N$ is a norm.
As for my thoughts? I am unable to apply the properties of the norm by proving so that N is not a norm in $C¹ [(0,1)]$ then indicate a subspace ${0} ≠ X ⊆ C¹ ([0, 1])$ in which $N$ is a norm.
functional-analysis banach-spaces
functional-analysis banach-spaces
edited Dec 6 '18 at 18:07
user334732
4,26311240
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
edited Dec 6 '18 at 18:07
user334732
4,26311240
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
edited Dec 6 '18 at 18:07
user334732
4,26311240
edited Dec 6 '18 at 18:07
user334732
4,26311240
edited Dec 6 '18 at 18:07
user334732
4,26311240
4,26311240
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
asked Dec 5 '18 at 21:03
Paulo Marcos RibeiroPaulo Marcos Ribeiro
61
61
closed as off-topic by GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138 Dec 6 '18 at 2:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138 Dec 6 '18 at 2:39
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – GNUSupporter 8964民主女神 地下教會, qbert, Lord_Farin, Chinnapparaj R, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
3
$begingroup$
Hi, what are your thoughts on the given problem ?
$endgroup$
– Rebellos
Dec 5 '18 at 21:05
$begingroup$
Hi, I am unable to apply the properties of the norm by proving so that N is not a norm in C¹ [(0,1)] then indicate a subspace {0} ≠ X ⊆ C¹ ([0, 1]) in which N is a norm.
$endgroup$
– Paulo Marcos Ribeiro
Dec 6 '18 at 10:25
$begingroup$
Hi Paulo and welcome to MSE. 1. Your thoughts on the problem, which you have added in a comment, you should add to the question itself, so the question fits site policies. 2. If you had pinged Rebellos by typing an "@" followed by his username he would have seen your comment.
$endgroup$
– user334732
Dec 6 '18 at 18:06
$begingroup$
And 3. you can use mathjax in comments. math.meta.stackexchange.com/questions/5020
$endgroup$
– user334732
Dec 6 '18 at 18:08
add a comment |
3
$begingroup$
Hi, what are your thoughts on the given problem ?
$endgroup$
– Rebellos
Dec 5 '18 at 21:05
$begingroup$
Hi, I am unable to apply the properties of the norm by proving so that N is not a norm in C¹ [(0,1)] then indicate a subspace {0} ≠ X ⊆ C¹ ([0, 1]) in which N is a norm.
$endgroup$
– Paulo Marcos Ribeiro
Dec 6 '18 at 10:25
$begingroup$
Hi Paulo and welcome to MSE. 1. Your thoughts on the problem, which you have added in a comment, you should add to the question itself, so the question fits site policies. 2. If you had pinged Rebellos by typing an "@" followed by his username he would have seen your comment.
$endgroup$
– user334732
Dec 6 '18 at 18:06
$begingroup$
And 3. you can use mathjax in comments. math.meta.stackexchange.com/questions/5020
$endgroup$
– user334732
Dec 6 '18 at 18:08
3
3
$begingroup$
Hi, what are your thoughts on the given problem ?
$endgroup$
– Rebellos
Dec 5 '18 at 21:05
$begingroup$
Hi, what are your thoughts on the given problem ?
$endgroup$
– Rebellos
Dec 5 '18 at 21:05
$begingroup$
Hi, I am unable to apply the properties of the norm by proving so that N is not a norm in C¹ [(0,1)] then indicate a subspace {0} ≠ X ⊆ C¹ ([0, 1]) in which N is a norm.
$endgroup$
– Paulo Marcos Ribeiro
Dec 6 '18 at 10:25
$begingroup$
Hi, I am unable to apply the properties of the norm by proving so that N is not a norm in C¹ [(0,1)] then indicate a subspace {0} ≠ X ⊆ C¹ ([0, 1]) in which N is a norm.
$endgroup$
– Paulo Marcos Ribeiro
Dec 6 '18 at 10:25
$begingroup$
Hi Paulo and welcome to MSE. 1. Your thoughts on the problem, which you have added in a comment, you should add to the question itself, so the question fits site policies. 2. If you had pinged Rebellos by typing an "@" followed by his username he would have seen your comment.
$endgroup$
– user334732
Dec 6 '18 at 18:06
$begingroup$
Hi Paulo and welcome to MSE. 1. Your thoughts on the problem, which you have added in a comment, you should add to the question itself, so the question fits site policies. 2. If you had pinged Rebellos by typing an "@" followed by his username he would have seen your comment.
$endgroup$
– user334732
Dec 6 '18 at 18:06
$begingroup$
And 3. you can use mathjax in comments. math.meta.stackexchange.com/questions/5020
$endgroup$
– user334732
Dec 6 '18 at 18:08
$begingroup$
And 3. you can use mathjax in comments. math.meta.stackexchange.com/questions/5020
$endgroup$
– user334732
Dec 6 '18 at 18:08
add a comment |
1 Answer
1
active
oldest
votes
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Hint
What do you think of $N(f_1)$ where $f_1$ is the constant function equal to $1$? Is $f_1$ always vanishing?
Then look at $X={f in mathcal C^1([0,1])| f(0)=0}$.
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint
What do you think of $N(f_1)$ where $f_1$ is the constant function equal to $1$? Is $f_1$ always vanishing?
Then look at $X={f in mathcal C^1([0,1])| f(0)=0}$.
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
$endgroup$
add a comment |
$begingroup$
Hint
What do you think of $N(f_1)$ where $f_1$ is the constant function equal to $1$? Is $f_1$ always vanishing?
Then look at $X={f in mathcal C^1([0,1])| f(0)=0}$.
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
$endgroup$
add a comment |
$begingroup$
Hint
What do you think of $N(f_1)$ where $f_1$ is the constant function equal to $1$? Is $f_1$ always vanishing?
Then look at $X={f in mathcal C^1([0,1])| f(0)=0}$.
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
$endgroup$
Hint
What do you think of $N(f_1)$ where $f_1$ is the constant function equal to $1$? Is $f_1$ always vanishing?
Then look at $X={f in mathcal C^1([0,1])| f(0)=0}$.
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
answered Dec 5 '18 at 21:08
mathcounterexamples.netmathcounterexamples.net
26k21955
26k21955
add a comment |
add a comment |
3
$begingroup$
Hi, what are your thoughts on the given problem ?
$endgroup$
– Rebellos
Dec 5 '18 at 21:05
$begingroup$
Hi, I am unable to apply the properties of the norm by proving so that N is not a norm in C¹ [(0,1)] then indicate a subspace {0} ≠ X ⊆ C¹ ([0, 1]) in which N is a norm.
$endgroup$
– Paulo Marcos Ribeiro
Dec 6 '18 at 10:25
$begingroup$
Hi Paulo and welcome to MSE. 1. Your thoughts on the problem, which you have added in a comment, you should add to the question itself, so the question fits site policies. 2. If you had pinged Rebellos by typing an "@" followed by his username he would have seen your comment.
$endgroup$
– user334732
Dec 6 '18 at 18:06
$begingroup$
And 3. you can use mathjax in comments. math.meta.stackexchange.com/questions/5020
$endgroup$
– user334732
Dec 6 '18 at 18:08