Closed hyperplanes on a normed space are isomorphic The 2019 Stack Overflow Developer Survey Results Are InIsometry from Banach Space to a Normed linear space mapsThe dual space of normed vector space $X$ is isomorphic to the dual of its completionFinite-dimensional subspace normed vector space is closedannihilator subspace of normed spaceSubspaces of same finite codimension are isomorphicTest of a normed vector space to be a direct sum with closed summandEvery separable Banach space is isomorphic to $ell_1/A$ for some closed $Asubset ell_1$is a normed space is always closed?Countable dimensional normed space incompleteProblem on Normed Linear Space
Can one be advised by a professor who is very far away?
Why isn't airport relocation done gradually?
What is the meaning of the verb "bear" in this context?
Is there a symbol for a right arrow with a square in the middle?
Did Scotland spend $250,000 for the slogan "Welcome to Scotland"?
Why did Acorn's A3000 have red function keys?
Multiply Two Integer Polynomials
A poker game description that does not feel gimmicky
Right tool to dig six foot holes?
What does Linus Torvalds mean when he says that Git "never ever" tracks a file?
What is the most effective way of iterating a std::vector and why?
What is the motivation for a law requiring 2 parties to consent for recording a conversation
Are there incongruent pythagorean triangles with the same perimeter and same area?
Can someone be penalized for an "unlawful" act if no penalty is specified?
When should I buy a clipper card after flying to OAK?
How to save as into a customized destination on macOS?
Delete all lines which don't have n characters before delimiter
How to type this arrow in math mode?
Do these rules for Critical Successes and Critical Failures seem Fair?
FPGA - DIY Programming
Worn-tile Scrabble
Is an up-to-date browser secure on an out-of-date OS?
What does ひと匙 mean in this manga and has it been used colloquially?
Shouldn't "much" here be used instead of "more"?
Closed hyperplanes on a normed space are isomorphic
The 2019 Stack Overflow Developer Survey Results Are InIsometry from Banach Space to a Normed linear space mapsThe dual space of normed vector space $X$ is isomorphic to the dual of its completionFinite-dimensional subspace normed vector space is closedannihilator subspace of normed spaceSubspaces of same finite codimension are isomorphicTest of a normed vector space to be a direct sum with closed summandEvery separable Banach space is isomorphic to $ell_1/A$ for some closed $Asubset ell_1$is a normed space is always closed?Countable dimensional normed space incompleteProblem on Normed Linear Space
$begingroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
15213
$endgroup$
add a comment |
$begingroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
15213
$endgroup$
add a comment |
$begingroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
15213
$endgroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
15213
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
15213
edited Apr 2 at 0:22
user71487
1088
edited Apr 2 at 0:22
user71487
1088
edited Apr 2 at 0:22
user71487
1088
1088
asked Mar 30 at 17:01
LucasLucas
15213
asked Mar 30 at 17:01
LucasLucas
15213
asked Mar 30 at 17:01
LucasLucas
15213
15213
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
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%2f3168525%2fclosed-hyperplanes-on-a-normed-space-are-isomorphic%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%2f3168525%2fclosed-hyperplanes-on-a-normed-space-are-isomorphic%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
