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Martin Sleziak
Martin Sleziak
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I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. Rørdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666 (MR1759891, jstor, author's homepage).

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!

I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. Rørdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666.

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!

I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. Rørdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666 (MR1759891, jstor, author's homepage).

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!

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Martin Sleziak
Martin Sleziak
  • 4.7k
  • 4
  • 35
  • 40

I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. R{\o}rdamRørdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666.

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!

I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. R{\o}rdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666.

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!

I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. Rørdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666.

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!

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Targaryen
Targaryen
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Pure infiniteness of tensor product $C^\ast$-algebras

I found the following theorem (Proposition 4.5) in the paper of E. Kirchberg and M. R{\o}rdam: Non-simple purely infinite $C^\ast$-algebras. Amer. J. Math. 122(3) (2000), 637-666.

Let $A$ be a unital, simple, separable, nuclear, purely infinite $C^\ast$-algebra, and let $B$ be any $C^\ast$-algebra. Then $A\otimes B$ is purely infinite.

My question is that can we drop the condition of nuclearity or separability of $A$ but the same conclusion still hold? Is there some known results?

I have searched in the literature but nothing founded.

Thank you very much for all helps!