The algebras of bounded operators on the Tsirelson and Baernstein spaces are not Grothendieck spaces

Kevin Beanland, Tomasz Kania, Niels Jakob Laustsen

We present 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^{\text…