This is an announcement for the paper "A reflexive space whose algebra of operators is not a Grothendieck" by Tomasz Kania.

Abstract: By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive space $(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_p}$ ($p\in (1,\infty))$, thus giving a negative answer to the problem posed in the monograph of Diestel and Uhl which asks whether the space of operators on a reflexive Banach space is Grothendieck.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 46B25, 47L10

Submitted from: t.kania@lancaster.ac.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1211.2867

or

http://arXiv.org/abs/1211.2867