
## 2. Calkin algebra

1. #### 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?
• #### Problem 2.2.

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