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Projective descriptions of weighted inductive limits: The vector-valued cases. (English) Zbl 0708.46037
Advances in the theory of Fréchet spaces, Proc. NATO Adv. Res. Workshop, Istanbul/Turkey 1988, NATO ASI Ser., Ser. C 287, 195-221 (1989).
Summary: [For the entire collection see Zbl 0699.00024.]
This is a report on some recent research on the projective description for weighted inductive limits of spaces of vector-valued continuous functions and on topological properties of vector-valued echelon and co- echelon spaces. In the first part, it is pointed out that most of the theorems known in the scalar case remain valid if the functions take values in a (DF)-space and that, similarly, many properties of the classical sequence spaces carry over to echelon spaces with values in a Fréchet space resp. to (DF)-space-valued co-echelon spaces. In the second part, we turn to the case that the continuous functions take their values in Fréchet spaces. This is related to some properties in the structure theory of Fréchet spaces and work by D. Vogt; part of the results in this direction are due to A. Galbis.

MSC:
46E40 Spaces of vector- and operator-valued functions
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46M40 Inductive and projective limits in functional analysis