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

Abstract

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 $p^{\text{th}}$ Baernstein space) for $p\in (1,\infty )$.

11 pp