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

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<mark>Journal publication date</mark>1/09/2019
<mark>Journal</mark>Houston Journal of Mathematics
Issue number2
Volume45
Number of pages13
Pages (from-to)553-566
Publication StatusE-pub ahead of print
Early online date1/09/19
<mark>Original language</mark>English

Abstract

We present two new examples of reflexive Banach spaces X for which the associated Banach algebra B(X) of bounded operators on X is not a Grothendieck space, namely X = T (the Tsirelson space) and X = Bp (the p'th Baernstein space) for 1<p<∞.