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Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
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When does the dual to the space $K(X)$ of compact operators consist of nuclear functionals?
This is the question of duality of injective and projective tensor products of Banach spaces, and the natural question would be whether the dual of $K(X)$ can be represented by the functionals in $N(X …