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

2. Calkin algebra


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      Problem 2.1.

      Is there a model of set theory in which the Calkin algebra has an automorphism sending the unilateral shift $S$ to $S^{\ast }$? Is the analogous fact for $\ell ^{\infty }\left/ c_{0}\right. $ true?


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          Problem 2.2.

          Is there a model of set theory in which the Calkin algebra has a not approximately inner automorphism preserving K-theory?


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              Problem 2.3.

              Is it consistent that, for a nonseparable Hilbert space $\mathcal{H}$, $\mathcal{B}\left( \mathcal{H}\right) \left/ \mathcal{K}\left( \mathcal{H}% \right) \right. $ has an outer automorphism?


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                  Problem 2.4.

                  [Anderson] Does every masa in the Calkin algebra that is generated by its projections lift to a masa in $\mathcal{B}\left( H\right) $?

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