The density condition in quotients of quasinormable Fréchet spaces. II (Q1300563)

With this paper, the author answers positively an open problem about the Heinrich density condition in quotients of Fréchet spaces. The problem was solved partially by the same author in part I [Stud. Math. 125, No. 2, 131-141 (1997; Zbl 0912.46001)], where she showed that a separable Fréchet space is quasinormable if, and only if, every quotient space satisfies the Heinrich density condition. Here the same statement is proved without the hypothesis of separability. The problem was proposed by \textit{J. Bonet} and \textit{J. C. Diaz}. They proved [Monatsh. Math. 117, No. 3-4, 199-212 (1994; Zbl 0804.46002)] that every Köthe echelon space of order \(p\) \((1< p<\infty)\) which is not quasinormable, has a separated quotient which does not satisfy the Heinrich density condition.