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Behaviour of Maximal tenor product with inductive limits

1

$begingroup$

I am trying to prove the following result:

Let $(A_i)_iin I$ be an inductive system of non unital $C^ast$-algebras with connecting homomorphisms $f_ij: A_i to A_j$ and let's denote the limit by $A$. If $B$ is another non unital $C^ast$-algebra, we would like to show that the inductive limit of $(A_iotimes_rmmax B)_iin I$ is isomorphic to $Aotimes_rmmax B$

I know the proof of this in case of unital $C^ast$-algebras but i cant see the proof for non unital case. Any ideas?

functional-analysis operator-theory c-star-algebras

share|cite|improve this question

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  what a coincidence, I am a tenor, too!
  $endgroup$
  – Alvin Lepik
  Apr 1 at 8:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AlvinLepik : Cheers!
  $endgroup$
  – Math Lover
  Apr 1 at 8:52
  

  
  
  
  

add a comment | 

1

$begingroup$

I am trying to prove the following result:

Let $(A_i)_iin I$ be an inductive system of non unital $C^ast$-algebras with connecting homomorphisms $f_ij: A_i to A_j$ and let's denote the limit by $A$. If $B$ is another non unital $C^ast$-algebra, we would like to show that the inductive limit of $(A_iotimes_rmmax B)_iin I$ is isomorphic to $Aotimes_rmmax B$

I know the proof of this in case of unital $C^ast$-algebras but i cant see the proof for non unital case. Any ideas?

functional-analysis operator-theory c-star-algebras

share|cite|improve this question

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  what a coincidence, I am a tenor, too!
  $endgroup$
  – Alvin Lepik
  Apr 1 at 8:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AlvinLepik : Cheers!
  $endgroup$
  – Math Lover
  Apr 1 at 8:52
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to prove the following result:

Let $(A_i)_iin I$ be an inductive system of non unital $C^ast$-algebras with connecting homomorphisms $f_ij: A_i to A_j$ and let's denote the limit by $A$. If $B$ is another non unital $C^ast$-algebra, we would like to show that the inductive limit of $(A_iotimes_rmmax B)_iin I$ is isomorphic to $Aotimes_rmmax B$

I know the proof of this in case of unital $C^ast$-algebras but i cant see the proof for non unital case. Any ideas?

functional-analysis operator-theory c-star-algebras

share|cite|improve this question

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315

$endgroup$

share|cite|improve this question

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315

share|cite|improve this question

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315

asked Apr 1 at 8:36

Math LoverMath Lover

1,044315