Loading Web-Font TeX/Math/Italic
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

2. Calkin algebra


    1. Add remark

      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?


        • Add remark

          Problem 2.2.

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


            • Add remark

              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?


                • Add remark

                  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.