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arXiv · 1707.08399

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

Kevin Beanland·Tomasz Kania·Niels Jakob Laustsen
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Abstract

We present two new examples of reflexive Banach spaces $X$ for which $\mathscr{B}(X)$ is not a Grothendieck space, namely $X = T$ (the Tsirelson space) and $X = B_p$ (the $p^{\text{th}}$ Baernstein space) for $p\in(1,\infty)$.

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Kevin Beanland, Tomasz Kania, Niels Jakob Laustsen. 2017-07-26. The algebras of bounded operators on the Tsirelson and Baernstein spaces are not Grothendieck spaces. https://arxiv.org/abs/1707.08399

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