Norms on Tensor Product of $C^*$- algebras












3












$begingroup$


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







share|cite|improve this question









$endgroup$

















    3












    $begingroup$


    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







    share|cite|improve this question









    $endgroup$















      3












      3








      3





      $begingroup$


      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







      share|cite|improve this question









      $endgroup$




      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






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 2 at 16:30









      Math LoverMath Lover

      958315




      958315






















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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.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Quite helpful,thanks
            $endgroup$
            – Math Lover
            Jan 3 at 6:01











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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.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Quite helpful,thanks
            $endgroup$
            – Math Lover
            Jan 3 at 6:01
















          2












          $begingroup$

          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.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Quite helpful,thanks
            $endgroup$
            – Math Lover
            Jan 3 at 6:01














          2












          2








          2





          $begingroup$

          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.






          share|cite|improve this answer









          $endgroup$



          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.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 2 at 17:38









          Martin ArgeramiMartin Argerami

          124k1177176




          124k1177176












          • $begingroup$
            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




          $begingroup$
          Quite helpful,thanks
          $endgroup$
          – Math Lover
          Jan 3 at 6:01


















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