Quojections and the problem of topologies of Grothendieck

Abstract

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 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.