examples of non-unital commutative $C^*$-algebras
$begingroup$
I know that all the non-unital commutative $C^*$ algebras are isomorphic to $C_0(Omega)$,where $Omega$ is a locally compact space.
Can anyone show me some common non-unital commutative examples.I only know the $c_0$ space.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
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add a comment |
$begingroup$
I know that all the non-unital commutative $C^*$ algebras are isomorphic to $C_0(Omega)$,where $Omega$ is a locally compact space.
Can anyone show me some common non-unital commutative examples.I only know the $c_0$ space.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
$endgroup$
1
$begingroup$
You already answered the question yourself.
$endgroup$
– user42761
Dec 12 '18 at 9:57
add a comment |
$begingroup$
I know that all the non-unital commutative $C^*$ algebras are isomorphic to $C_0(Omega)$,where $Omega$ is a locally compact space.
Can anyone show me some common non-unital commutative examples.I only know the $c_0$ space.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
$endgroup$
I know that all the non-unital commutative $C^*$ algebras are isomorphic to $C_0(Omega)$,where $Omega$ is a locally compact space.
Can anyone show me some common non-unital commutative examples.I only know the $c_0$ space.
operator-theory operator-algebras c-star-algebras von-neumann-algebras
operator-theory operator-algebras c-star-algebras von-neumann-algebras
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
edited Dec 13 '18 at 6:16
mathrookie
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
asked Dec 12 '18 at 0:35
mathrookiemathrookie
899512
899512
1
$begingroup$
You already answered the question yourself.
$endgroup$
– user42761
Dec 12 '18 at 9:57
add a comment |
1
$begingroup$
You already answered the question yourself.
$endgroup$
– user42761
Dec 12 '18 at 9:57
1
1
$begingroup$
You already answered the question yourself.
$endgroup$
– user42761
Dec 12 '18 at 9:57
$begingroup$
You already answered the question yourself.
$endgroup$
– user42761
Dec 12 '18 at 9:57
add a comment |
1 Answer
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$begingroup$
The algebra $c_0$ is $C_0(mathbb N)$. All you need is other examples of non-compact, locally compact spaces. The next familiar one is $mathbb R$. Or $mathbb R^n$ for any $ninmathbb N$.
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
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1 Answer
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$begingroup$
The algebra $c_0$ is $C_0(mathbb N)$. All you need is other examples of non-compact, locally compact spaces. The next familiar one is $mathbb R$. Or $mathbb R^n$ for any $ninmathbb N$.
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
$endgroup$
add a comment |
$begingroup$
The algebra $c_0$ is $C_0(mathbb N)$. All you need is other examples of non-compact, locally compact spaces. The next familiar one is $mathbb R$. Or $mathbb R^n$ for any $ninmathbb N$.
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
$endgroup$
add a comment |
$begingroup$
The algebra $c_0$ is $C_0(mathbb N)$. All you need is other examples of non-compact, locally compact spaces. The next familiar one is $mathbb R$. Or $mathbb R^n$ for any $ninmathbb N$.
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
$endgroup$
The algebra $c_0$ is $C_0(mathbb N)$. All you need is other examples of non-compact, locally compact spaces. The next familiar one is $mathbb R$. Or $mathbb R^n$ for any $ninmathbb N$.
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
answered Dec 12 '18 at 15:21
Martin ArgeramiMartin Argerami
127k1182182
127k1182182
add a comment |
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You already answered the question yourself.
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– user42761
Dec 12 '18 at 9:57