(LF)-SPACES AND TENSOR-PRODUCTS

For a countable inductive limit of metrizable locally convex spaces, a condition (M) (in the sense of RETAKH) by operators is introduced and the incidence of this property for the interchangeability of (LF)-spa ces and tensor products with a Banach space is discussed. Examples are given in the setting of weighted (LF)-spaces of continuous functions, Kothe (LF)-sequence spaces, weighted (LB)-spaces of holomorphic funct ions on balanced domains.