finite dimensional $C^*$ subalgebra
$begingroup$
Given any $C^*$-algebra $A$ (not necessarily unital),can we construct a nonzero finite dimensional $C^*$-subalgebra of $A$?
operator-theory operator-algebras c-star-algebras
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
$endgroup$
add a comment |
$begingroup$
Given any $C^*$-algebra $A$ (not necessarily unital),can we construct a nonzero finite dimensional $C^*$-subalgebra of $A$?
operator-theory operator-algebras c-star-algebras
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
$endgroup$
add a comment |
$begingroup$
Given any $C^*$-algebra $A$ (not necessarily unital),can we construct a nonzero finite dimensional $C^*$-subalgebra of $A$?
operator-theory operator-algebras c-star-algebras
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
$endgroup$
Given any $C^*$-algebra $A$ (not necessarily unital),can we construct a nonzero finite dimensional $C^*$-subalgebra of $A$?
operator-theory operator-algebras c-star-algebras
operator-theory operator-algebras c-star-algebras
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
asked Dec 31 '18 at 18:38
mathrookiemathrookie
916512
916512
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No. Every finite dimensional $C^*$-algebra is a von Neumann algebra, because it is a Banach dual space. $W^*$ algebras contain many projections -- in particular the range projections of their elements -- but there are $C^*$-algebras with no projections.
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
$endgroup$
add a comment |
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%2f3057941%2ffinite-dimensional-c-subalgebra%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
$begingroup$
No. Every finite dimensional $C^*$-algebra is a von Neumann algebra, because it is a Banach dual space. $W^*$ algebras contain many projections -- in particular the range projections of their elements -- but there are $C^*$-algebras with no projections.
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
$endgroup$
add a comment |
$begingroup$
No. Every finite dimensional $C^*$-algebra is a von Neumann algebra, because it is a Banach dual space. $W^*$ algebras contain many projections -- in particular the range projections of their elements -- but there are $C^*$-algebras with no projections.
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
$endgroup$
add a comment |
$begingroup$
No. Every finite dimensional $C^*$-algebra is a von Neumann algebra, because it is a Banach dual space. $W^*$ algebras contain many projections -- in particular the range projections of their elements -- but there are $C^*$-algebras with no projections.
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
$endgroup$
No. Every finite dimensional $C^*$-algebra is a von Neumann algebra, because it is a Banach dual space. $W^*$ algebras contain many projections -- in particular the range projections of their elements -- but there are $C^*$-algebras with no projections.
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
answered Dec 31 '18 at 21:02
Ashwin TrisalAshwin Trisal
1,2891516
1,2891516
add a comment |
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%2f3057941%2ffinite-dimensional-c-subalgebra%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
