* b(X´, X) denotes the topology of bounded convergence on X´ or the strong dual topology on X´ and or denotes ''X''´ endowed with this topology.
** As usual, if X* is considered as a topological vector space but it has not been made clear what topology it is endowed with, then the topology will be assumed to be b(X´, X).

A canonical tensor product as a subspace of the dual of Bi(X, Y)

Let

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