Find completion of polynomial equipped with norm Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Completion of Topological Group with Metric$p$-adic completion of integersDoes a norm have to map to $mathbb R$?Proof metric space with distance functionExplicit delta for polynomial limitMetric completion of polynomial function spaceCompletion of polynomial space with max normBounded Lipschitz function space is separable for uniform normShow that $mathcalA$ is dense in $C([0,2016])$.The space of all finite-degree polynomials $mathbbP$ is not complete in any norm.
Storing hydrofluoric acid before the invention of plastics
How can I make names more distinctive without making them longer?
IndentationError when pasting code in Python 3 interpreter mode
3 doors, three guards, one stone
How does cp -a work
WAN encapsulation
What happens to sewage if there is no river near by?
What is the longest distance a 13th-level monk can jump while attacking on the same turn?
Why are there no cargo aircraft with "flying wing" design?
How can I fade player when goes inside or outside of the area?
Why did the IBM 650 use bi-quinary?
Is it true to say that an hosting provider's DNS server is what links the entire hosting environment to ICANN?
What LEGO pieces have "real-world" functionality?
If Jon Snow became King of the Seven Kingdoms what would his regnal number be?
Gastric acid as a weapon
Is 1 ppb equal to 1 μg/kg?
How do I mention the quality of my school without bragging
Output the ŋarâþ crîþ alphabet song without using (m)any letters
Check which numbers satisfy the condition [A*B*C = A! + B! + C!]
Is it possible to boil a liquid by just mixing many immiscible liquids together?
If a contract sometimes uses the wrong name, is it still valid?
How discoverable are IPv6 addresses and AAAA names by potential attackers?
Does polymorph use a PC’s CR or its level?
Can Pao de Queijo, and similar foods, be kosher for Passover?
Find completion of polynomial equipped with norm
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Completion of Topological Group with Metric$p$-adic completion of integersDoes a norm have to map to $mathbb R$?Proof metric space with distance functionExplicit delta for polynomial limitMetric completion of polynomial function spaceCompletion of polynomial space with max normBounded Lipschitz function space is separable for uniform normShow that $mathcalA$ is dense in $C([0,2016])$.The space of all finite-degree polynomials $mathbbP$ is not complete in any norm.
$begingroup$
Let $mathcalP$ denote the space of polynomials with respect to the norm $$| a_0 + a_1 x + dots + a_nx^n| = |a_0| + |a_1| + dots + |a_n|.$$ Determine the completion of $mathcalP$.
I've never seen an example actually computing the completion of something, so I really don't know where to start
Thanks
analysis metric-spaces
asked Mar 26 at 6:44
yyyyyyyy
82
$endgroup$
add a comment |
$begingroup$
Let $mathcalP$ denote the space of polynomials with respect to the norm $$| a_0 + a_1 x + dots + a_nx^n| = |a_0| + |a_1| + dots + |a_n|.$$ Determine the completion of $mathcalP$.
I've never seen an example actually computing the completion of something, so I really don't know where to start
Thanks
analysis metric-spaces
asked Mar 26 at 6:44
yyyyyyyy
82
$endgroup$
add a comment |
$begingroup$
Let $mathcalP$ denote the space of polynomials with respect to the norm $$| a_0 + a_1 x + dots + a_nx^n| = |a_0| + |a_1| + dots + |a_n|.$$ Determine the completion of $mathcalP$.
I've never seen an example actually computing the completion of something, so I really don't know where to start
Thanks
analysis metric-spaces
asked Mar 26 at 6:44
yyyyyyyy
82
$endgroup$
Let $mathcalP$ denote the space of polynomials with respect to the norm $$| a_0 + a_1 x + dots + a_nx^n| = |a_0| + |a_1| + dots + |a_n|.$$ Determine the completion of $mathcalP$.
I've never seen an example actually computing the completion of something, so I really don't know where to start
Thanks
analysis metric-spaces
analysis metric-spaces
asked Mar 26 at 6:44
yyyyyyyy
82
asked Mar 26 at 6:44
yyyyyyyy
82
asked Mar 26 at 6:44
yyyyyyyy
82
asked Mar 26 at 6:44
yyyyyyyy
82
asked Mar 26 at 6:44
yyyyyyyy
82
82
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Modification of Theo Bendit's answer:
Hint: show that this space is isometrically isomorphic to c00, the space of real sequences with finite support, under the $Vert Vert_1$ norm, where $Vert a Vert_1:=sum_n vert a_nvert$. Then find a Banach Space in which c00 is a dense subspace.
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
$endgroup$
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
add a comment |
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%2f3162813%2ffind-completion-of-polynomial-equipped-with-norm%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Modification of Theo Bendit's answer:
Hint: show that this space is isometrically isomorphic to c00, the space of real sequences with finite support, under the $Vert Vert_1$ norm, where $Vert a Vert_1:=sum_n vert a_nvert$. Then find a Banach Space in which c00 is a dense subspace.
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
$endgroup$
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
add a comment |
$begingroup$
Modification of Theo Bendit's answer:
Hint: show that this space is isometrically isomorphic to c00, the space of real sequences with finite support, under the $Vert Vert_1$ norm, where $Vert a Vert_1:=sum_n vert a_nvert$. Then find a Banach Space in which c00 is a dense subspace.
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
$endgroup$
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
add a comment |
$begingroup$
Modification of Theo Bendit's answer:
Hint: show that this space is isometrically isomorphic to c00, the space of real sequences with finite support, under the $Vert Vert_1$ norm, where $Vert a Vert_1:=sum_n vert a_nvert$. Then find a Banach Space in which c00 is a dense subspace.
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
$endgroup$
Modification of Theo Bendit's answer:
Hint: show that this space is isometrically isomorphic to c00, the space of real sequences with finite support, under the $Vert Vert_1$ norm, where $Vert a Vert_1:=sum_n vert a_nvert$. Then find a Banach Space in which c00 is a dense subspace.
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
answered Mar 26 at 7:38
Jens SchwaigerJens Schwaiger
1,639138
1,639138
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
add a comment |
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
$begingroup$
Obviously Theo Bendit's answer has been deleted.
$endgroup$
– Jens Schwaiger
Mar 27 at 6:31
add a comment |
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%2f3162813%2ffind-completion-of-polynomial-equipped-with-norm%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
