The subspace problem for weighted inductive limits revisited

We construct a countable inductive limit of weighted Banach spaces of holom orphic functions on an open subset of C-2 which has a topology that cannot be described canonically by weighted sup-seminorms but such that the sequen ce of weights is regularly decreasing in the sense of Bierstedt, Meise and Summers. This solves an open problem of these authors from 1986.