This is an announcement for the paper “The algebras of bounded operators on the Tsirelson and Baernstein spaces are not Grothendieck spaces” by Kevin Beanlandhttps://arxiv.org/find/math/1/au:+Beanland_K/0/1/0/all/0/1, Tomasz Kaniahttps://arxiv.org/find/math/1/au:+Kania_T/0/1/0/all/0/1, Niels Jakob Laustsenhttps://arxiv.org/find/math/1/au:+Laustsen_N/0/1/0/all/0/1.
Abstract: We show that if the Banach algebra $\mathcal{B}(X)$ of bounded operators on a Banach space $X$ is a Grothendieck space, then $X$ is reflexive, and we give two new examples of reflexive Banach spaces $X$ for which $\mathcal{B}(X)$ is not a Grothendieck space, namely $X=T$ (the Tsirelson space) and $X=B_p$(the $p$th Baernstein space) for $p\in (1, \infty)$.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1707.08399