Immersion duals spaces The 2019 Stack Overflow Developer Survey Results Are In Unicorn Meta Zoo #1: Why another podcast? Announcing the arrival of Valued Associate #679: Cesar ManaraProperties of dual spaces of sequence spacesCountable total subset in $ell^infty/ c_0$on the no existence of a continuous extension of the identity function on $c_0$ to $l^infty$ not equal to $I$When is an operator on $ell_1$ the dual of an operator on $c_0$?Examples of double dual spacesExample (?) of a Banach space containing an uncomplemented copy of itselfExistence of specific weak derivativeA normed space is not separable when $ell_infty$ can be embedded isometrically into itMy attempt to show the canonical embedding $c_0rightarrow c_0^**$ is not surjective?How to show a diagram commutes?
What to do when moving next to a bird sanctuary with a loosely-domesticated cat?
Define a list range inside a list
ELI5: Why do they say that Israel would have been the fourth country to land a spacecraft on the Moon and why do they call it low cost?
For what reasons would an animal species NOT cross a *horizontal* land bridge?
Why doesn't shell automatically fix "useless use of cat"?
Why did Peik Lin say, "I'm not an animal"?
Why can't devices on different VLANs, but on the same subnet, communicate?
Do I have Disadvantage attacking with an off-hand weapon?
Homework question about an engine pulling a train
My body leaves; my core can stay
Can we generate random numbers using irrational numbers like π and e?
Is an up-to-date browser secure on an out-of-date OS?
Could an empire control the whole planet with today's comunication methods?
Why don't hard Brexiteers insist on a hard border to prevent illegal immigration after Brexit?
Why doesn't a hydraulic lever violate conservation of energy?
Intergalactic human space ship encounters another ship, character gets shunted off beyond known universe, reality starts collapsing
What can I do if neighbor is blocking my solar panels intentionally?
How do I design a circuit to convert a 100 mV and 50 Hz sine wave to a square wave?
Did the new image of black hole confirm the general theory of relativity?
Example of compact Riemannian manifold with only one geodesic.
Can a flute soloist sit?
How to politely respond to generic emails requesting a PhD/job in my lab? Without wasting too much time
What information about me do stores get via my credit card?
What is the padding with red substance inside of steak packaging?
Immersion duals spaces
The 2019 Stack Overflow Developer Survey Results Are In
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraProperties of dual spaces of sequence spacesCountable total subset in $ell^infty/ c_0$on the no existence of a continuous extension of the identity function on $c_0$ to $l^infty$ not equal to $I$When is an operator on $ell_1$ the dual of an operator on $c_0$?Examples of double dual spacesExample (?) of a Banach space containing an uncomplemented copy of itselfExistence of specific weak derivativeA normed space is not separable when $ell_infty$ can be embedded isometrically into itMy attempt to show the canonical embedding $c_0rightarrow c_0^**$ is not surjective?How to show a diagram commutes?
$begingroup$
Is correct say that $(ell_infty)'subset (c_0)'$?
My idea is the following:
I know that $c_0subsetell_infty$. Then, the function
$$
beginsplit
Psi:(ell_infty)'&to(c_0)'\
f&mapstoPsi(f)=f|_c_0
endsplit
$$
is injective.
Is correct the function? Does exist an injective function $Psi$ such that $(ell_infty)'subset (c_0)'$?
real-analysis functional-analysis banach-spaces
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
$endgroup$
add a comment |
$begingroup$
Is correct say that $(ell_infty)'subset (c_0)'$?
My idea is the following:
I know that $c_0subsetell_infty$. Then, the function
$$
beginsplit
Psi:(ell_infty)'&to(c_0)'\
f&mapstoPsi(f)=f|_c_0
endsplit
$$
is injective.
Is correct the function? Does exist an injective function $Psi$ such that $(ell_infty)'subset (c_0)'$?
real-analysis functional-analysis banach-spaces
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
$endgroup$
$begingroup$
what is $c_0$ in your question?
$endgroup$
– Pink Panther
Apr 8 at 6:51
$begingroup$
$ell_infty^*$'s cardinality exceeds that of the continuum; the same can't be said for $c_0^*=ell_1$'s cardinality.
$endgroup$
– David Mitra
Apr 8 at 11:10
$begingroup$
The restriction map you define is NOT injective! This is not completely obvious but follows from the Hahn-Banach theorem.
$endgroup$
– Jochen
Apr 9 at 7:47
add a comment |
$begingroup$
Is correct say that $(ell_infty)'subset (c_0)'$?
My idea is the following:
I know that $c_0subsetell_infty$. Then, the function
$$
beginsplit
Psi:(ell_infty)'&to(c_0)'\
f&mapstoPsi(f)=f|_c_0
endsplit
$$
is injective.
Is correct the function? Does exist an injective function $Psi$ such that $(ell_infty)'subset (c_0)'$?
real-analysis functional-analysis banach-spaces
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
$endgroup$
Is correct say that $(ell_infty)'subset (c_0)'$?
My idea is the following:
I know that $c_0subsetell_infty$. Then, the function
$$
beginsplit
Psi:(ell_infty)'&to(c_0)'\
f&mapstoPsi(f)=f|_c_0
endsplit
$$
is injective.
Is correct the function? Does exist an injective function $Psi$ such that $(ell_infty)'subset (c_0)'$?
real-analysis functional-analysis banach-spaces
real-analysis functional-analysis banach-spaces
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
edited Apr 8 at 6:38
Daniele Tampieri
2,69721022
2,69721022
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
asked Apr 8 at 6:25
Jose EsparragoJose Esparrago
162
162
$begingroup$
what is $c_0$ in your question?
$endgroup$
– Pink Panther
Apr 8 at 6:51
$begingroup$
$ell_infty^*$'s cardinality exceeds that of the continuum; the same can't be said for $c_0^*=ell_1$'s cardinality.
$endgroup$
– David Mitra
Apr 8 at 11:10
$begingroup$
The restriction map you define is NOT injective! This is not completely obvious but follows from the Hahn-Banach theorem.
$endgroup$
– Jochen
Apr 9 at 7:47
add a comment |
$begingroup$
what is $c_0$ in your question?
$endgroup$
– Pink Panther
Apr 8 at 6:51
$begingroup$
$ell_infty^*$'s cardinality exceeds that of the continuum; the same can't be said for $c_0^*=ell_1$'s cardinality.
$endgroup$
– David Mitra
Apr 8 at 11:10
$begingroup$
The restriction map you define is NOT injective! This is not completely obvious but follows from the Hahn-Banach theorem.
$endgroup$
– Jochen
Apr 9 at 7:47
$begingroup$
what is $c_0$ in your question?
$endgroup$
– Pink Panther
Apr 8 at 6:51
$begingroup$
what is $c_0$ in your question?
$endgroup$
– Pink Panther
Apr 8 at 6:51
$begingroup$
$ell_infty^*$'s cardinality exceeds that of the continuum; the same can't be said for $c_0^*=ell_1$'s cardinality.
$endgroup$
– David Mitra
Apr 8 at 11:10
$begingroup$
$ell_infty^*$'s cardinality exceeds that of the continuum; the same can't be said for $c_0^*=ell_1$'s cardinality.
$endgroup$
– David Mitra
Apr 8 at 11:10
$begingroup$
The restriction map you define is NOT injective! This is not completely obvious but follows from the Hahn-Banach theorem.
$endgroup$
– Jochen
Apr 9 at 7:47
$begingroup$
The restriction map you define is NOT injective! This is not completely obvious but follows from the Hahn-Banach theorem.
$endgroup$
– Jochen
Apr 9 at 7:47
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3179248%2fimmersion-duals-spaces%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3179248%2fimmersion-duals-spaces%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
what is $c_0$ in your question?
$endgroup$
– Pink Panther
Apr 8 at 6:51
$begingroup$
$ell_infty^*$'s cardinality exceeds that of the continuum; the same can't be said for $c_0^*=ell_1$'s cardinality.
$endgroup$
– David Mitra
Apr 8 at 11:10
$begingroup$
The restriction map you define is NOT injective! This is not completely obvious but follows from the Hahn-Banach theorem.
$endgroup$
– Jochen
Apr 9 at 7:47