The density condition in projective tensor products (Q1974103)

The density condition was introduced by S. Heinrich in the context of ultrapowers of locally convex spaces in 1984. It was investigated thoroughly for Fréchet spaces, together with the dual density condition for (DF)-spaces in a series of articles by K. D. Bierstedt and the reviewer in 1986-1990. The author presents a characterization of the dual density condition for spaces of continuous linear operators from a Banach space into the strong dual of a Fréchet space. A modification of Taskinen's original counterexample from 1986 to the problem of topologies of Grothendieck permits the author to construct a Fréchet space \(F\) with the density condition such that the space of operators \(L_b(\ell_2, F_b')\) does not satisfy the dual density condition.