Abstract of a paper by Kevin Beanland, Tomasz Kania, Niels Jakob Laustsen
This is an announcement for the paper “The algebras of bounded operators on the Tsirelson and Baernstein spaces are not Grothendieck spaces” by Kevin Beanland<https://arxiv.org/find/math/1/au:+Beanland_K/0/1/0/all/0/1>, Tomasz Kania<https://arxiv.org/find/math/1/au:+Kania_T/0/1/0/all/0/1>, Niels Jakob Laustsen<https://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
participants (1)
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Bentuo Zheng (bzheng)