When is $ overline {T(B)}$ compact? [closed]
$begingroup$
Let $V$ and $W$ be normed linear spaces and let $ T : V to W$ be a continuous linear operator. Let $B$ be the closed unit ball in $V$ . In which of the
following cases is $ overline {T(B)}$ compact?
$ V = C^1[0, 1],W = C[0, 1]$ and $T(f) = f$.
$V = W = l_2$ and $T(x) = (0,x_1,x_2,ldots)$, where $x = (x_n)in l_2$.
$V = W = l_2$ and $T(x) = (x_1, x_2,x_{10}, 0, 0,0,ldots)$, where $x = (x_n)in l_2$.
This is a question from a PhD entrance exam,I cant show any work.
I am sorry for that,Can you kindly give some hints
functional-analysis compactness
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
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closed as off-topic by Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy Dec 28 '18 at 7:33
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." – Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $V$ and $W$ be normed linear spaces and let $ T : V to W$ be a continuous linear operator. Let $B$ be the closed unit ball in $V$ . In which of the
following cases is $ overline {T(B)}$ compact?
$ V = C^1[0, 1],W = C[0, 1]$ and $T(f) = f$.
$V = W = l_2$ and $T(x) = (0,x_1,x_2,ldots)$, where $x = (x_n)in l_2$.
$V = W = l_2$ and $T(x) = (x_1, x_2,x_{10}, 0, 0,0,ldots)$, where $x = (x_n)in l_2$.
This is a question from a PhD entrance exam,I cant show any work.
I am sorry for that,Can you kindly give some hints
functional-analysis compactness
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
$endgroup$
closed as off-topic by Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy Dec 28 '18 at 7:33
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." – Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $V$ and $W$ be normed linear spaces and let $ T : V to W$ be a continuous linear operator. Let $B$ be the closed unit ball in $V$ . In which of the
following cases is $ overline {T(B)}$ compact?
$ V = C^1[0, 1],W = C[0, 1]$ and $T(f) = f$.
$V = W = l_2$ and $T(x) = (0,x_1,x_2,ldots)$, where $x = (x_n)in l_2$.
$V = W = l_2$ and $T(x) = (x_1, x_2,x_{10}, 0, 0,0,ldots)$, where $x = (x_n)in l_2$.
This is a question from a PhD entrance exam,I cant show any work.
I am sorry for that,Can you kindly give some hints
functional-analysis compactness
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
$endgroup$
Let $V$ and $W$ be normed linear spaces and let $ T : V to W$ be a continuous linear operator. Let $B$ be the closed unit ball in $V$ . In which of the
following cases is $ overline {T(B)}$ compact?
$ V = C^1[0, 1],W = C[0, 1]$ and $T(f) = f$.
$V = W = l_2$ and $T(x) = (0,x_1,x_2,ldots)$, where $x = (x_n)in l_2$.
$V = W = l_2$ and $T(x) = (x_1, x_2,x_{10}, 0, 0,0,ldots)$, where $x = (x_n)in l_2$.
This is a question from a PhD entrance exam,I cant show any work.
I am sorry for that,Can you kindly give some hints
functional-analysis compactness
functional-analysis compactness
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
asked Dec 24 '18 at 9:37
Join_PhDJoin_PhD
4018
4018
closed as off-topic by Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy Dec 28 '18 at 7:33
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." – Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy Dec 28 '18 at 7:33
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." – Math_QED, Nosrati, RRL, amWhy, Kavi Rama Murthy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
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