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\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

3. Tensor products


    1. Add remark

      Problem 3.1.

      Does the number of C*-norms on $A\otimes _{alg}B$ for

      • $A=B=\mathcal{B}\left( H\right) $

      • $A=B=C^{\ast }\left( \mathbb{F}_{\infty }\right) $, where $\mathbb{F}% _{\infty }$ is the free group on countably many generators

      • $A=B\left( H\right) $ and $B=\mathcal{Q}\left( H\right) $ where $% \mathcal{Q}\left( H\right) $ is the Calkin algebra


      depend on the model of set theory?


        • Add remark

          Problem 3.2.

          What is the ideal structure of $\mathcal{B}\left( H\right) \otimes _{\min }\mathcal{Q}\left( H\right) $? Does it depend on the model of set theory?


            • Add remark

              Problem 3.3.

              Does $\otimes _{\min }$ or $\otimes _{\max }$ commute with forcing?

                  Cite this as: AimPL: Set theory and C* algebras, available at http://aimpl.org/settheorycstar.