Abstract:The example of a nuclear Fréchet space E is given, for which the space L(E, E) of bounded linear operators on E, when endowed with the topology of uniform convergence on bounded sets, is not bornological. It is shown further that for E the subspace of the product R I over an uncountable index set I formed by the sequences with countable support, this locally convex topology on the space L(E, E) is bornological.
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