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§3] produced an expository list of such questions in 1973. It is remarkable how few of these questions that have been resolved in the meantime. We shall make a small contribution towards the resolution of the seemingly very difficult problem of describing the Banach spaces X for which the associated Banach algebra B(X) of bounded operators on X is a Grothendieck space by proving the following result. th Theorem 1.1. Let X be either the Tsirelson space T or the p Baernstein space Bp, where 1
n Theorem 1.2 (Kania). Let X = ∈N ℓq , where 1