This is an announcement for the paper “Weak closure of ultrapowers of operators on $L_p$” by March Boedihardjohttps://arxiv.org/find/math/1/au:+Boedihardjo_M/0/1/0/all/0/1.

Abstract: Let $1<p<\infty$. We find the closure of ultrapowers of operators on $L_p$ in the weak operator topology when the ultrafilter is selective. As a consequence, we show that the commutant of $B(L_p)$ in its ultrapower may or may not be trivial depending on the ultrafilter assuming the existence of a selective nonprincipal ultrafilter. This extends a result of Farah, Phillips and Stepr=ans.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1707.09658