Quojections and the problem of topologies of Grothendieck


We show that the problem of topologies of Grothendieck has a negative answer in the case of quojections: we construct a separable reflexive quojection E such that E\widehat{⨂}_𝜋 l<sup>2</sup> does not have property (BB) in the sense of [T1]. This result implies for example the existence of a strict (LB)-space without a local partition of unity in the sense of Hollstein.

DOI Code: 10.1285/i15900932v11p49

Classification: 46M05

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