Mixing
Norms on Tensor Product of $C^*$- algebras
$begingroup$
Suppose $A$ and $B$ are two $C^*$-algebras. On the algebraic tensor product $Aotimes B$ we can define the maximal and minimal tensor norms which makes $Aotimes B$ a $C^*$- algebra.
what are other possible norms which one define on algebraic tensor product of $C^*-$ algebras to make it again a $C^*$ -algebra?
The books I have seen only discusses these two norms while they do discuss many norms on tensor product of operator spaces.Why so?
functional-analysis operator-theory tensor-products c-star-algebras
asked Jan 2 at 16:30
Math LoverMath Lover
958315
$endgroup$
add a comment |
$begingroup$
Suppose $A$ and $B$ are two $C^*$-algebras. On the algebraic tensor product $Aotimes B$ we can define the maximal and minimal tensor norms which makes $Aotimes B$ a $C^*$- algebra.
what are other possible norms which one define on algebraic tensor product of $C^*-$ algebras to make it again a $C^*$ -algebra?
The books I have seen only discusses these two norms while they do discuss many norms on tensor product of operator spaces.Why so?
functional-analysis operator-theory tensor-products c-star-algebras
asked Jan 2 at 16:30
Math LoverMath Lover
958315
$endgroup$
add a comment |
$begingroup$
Suppose $A$ and $B$ are two $C^*$-algebras. On the algebraic tensor product $Aotimes B$ we can define the maximal and minimal tensor norms which makes $Aotimes B$ a $C^*$- algebra.
what are other possible norms which one define on algebraic tensor product of $C^*-$ algebras to make it again a $C^*$ -algebra?
The books I have seen only discusses these two norms while they do discuss many norms on tensor product of operator spaces.Why so?
functional-analysis operator-theory tensor-products c-star-algebras
asked Jan 2 at 16:30
Math LoverMath Lover
958315
$endgroup$
Suppose $A$ and $B$ are two $C^*$-algebras. On the algebraic tensor product $Aotimes B$ we can define the maximal and minimal tensor norms which makes $Aotimes B$ a $C^*$- algebra.
what are other possible norms which one define on algebraic tensor product of $C^*-$ algebras to make it again a $C^*$ -algebra?
The books I have seen only discusses these two norms while they do discuss many norms on tensor product of operator spaces.Why so?
functional-analysis operator-theory tensor-products c-star-algebras
functional-analysis operator-theory tensor-products c-star-algebras
asked Jan 2 at 16:30
Math LoverMath Lover
958315
asked Jan 2 at 16:30
Math LoverMath Lover
958315
asked Jan 2 at 16:30
Math LoverMath Lover
958315
asked Jan 2 at 16:30
Math LoverMath Lover
958315
asked Jan 2 at 16:30
Math LoverMath Lover
958315
958315
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Because, as far as I can tell, there is no general recipe to produce a C$^*$-norm on $Aotimes B$ other than the max and the min norms. And for all nuclear algebras $A$ you have that the max and the min norm are equal, so in general you cannot expect to find a "different" one.
With operator spaces and operator systems, as opposed to the case with C$^*$-algebras, there seems to be several natural ways to produce tensor norms.
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
$endgroup$
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
add a comment |
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$begingroup$
Because, as far as I can tell, there is no general recipe to produce a C$^*$-norm on $Aotimes B$ other than the max and the min norms. And for all nuclear algebras $A$ you have that the max and the min norm are equal, so in general you cannot expect to find a "different" one.
With operator spaces and operator systems, as opposed to the case with C$^*$-algebras, there seems to be several natural ways to produce tensor norms.
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
$endgroup$
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
add a comment |
$begingroup$
Because, as far as I can tell, there is no general recipe to produce a C$^*$-norm on $Aotimes B$ other than the max and the min norms. And for all nuclear algebras $A$ you have that the max and the min norm are equal, so in general you cannot expect to find a "different" one.
With operator spaces and operator systems, as opposed to the case with C$^*$-algebras, there seems to be several natural ways to produce tensor norms.
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
$endgroup$
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
add a comment |
$begingroup$
Because, as far as I can tell, there is no general recipe to produce a C$^*$-norm on $Aotimes B$ other than the max and the min norms. And for all nuclear algebras $A$ you have that the max and the min norm are equal, so in general you cannot expect to find a "different" one.
With operator spaces and operator systems, as opposed to the case with C$^*$-algebras, there seems to be several natural ways to produce tensor norms.
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
$endgroup$
Because, as far as I can tell, there is no general recipe to produce a C$^*$-norm on $Aotimes B$ other than the max and the min norms. And for all nuclear algebras $A$ you have that the max and the min norm are equal, so in general you cannot expect to find a "different" one.
With operator spaces and operator systems, as opposed to the case with C$^*$-algebras, there seems to be several natural ways to produce tensor norms.
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
answered Jan 2 at 17:38
Martin ArgeramiMartin Argerami
124k1177176
124k1177176
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
add a comment |
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
$begingroup$
Quite helpful,thanks
$endgroup$
– Math Lover
Jan 3 at 6:01
add a comment |
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