Approximationseigenschaft,Lifting und Kohomologie bei lokalkonvexen Produktgarben

Motivated by examples like spaces of solutions of hypoelliptic operators, we treat product sheaves, prove density theorems in connection with the approximation property and use them for results on liftings and the vanishing of cohomology groups. Theorems of this type (2.4,2.9,3.3) are derived on regular subsets (2.3) of a product for product sheaves, where one factor has essentially a partition of unity. In the case of the compact open topology, we obtain the approximation property on arbitrary open subsets by a localization principle (4.5,4.9). The nuclearity of a sheaf in the co-topology turns out to imply strong nuclearity (1.11); the same is shown for the sheaf of holomorphic functions on the dual of a strongly nuclear (F)-space (1.12).

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Herrn Professor Gottfried Köthe zum 70. Geburtstag gewidmet