An example of two distinguished M c h e t spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E&F is not distinguished. On the other hand, it is proved that for arbitrary reflexive F r k h e t space E and arbitrary compact set K the space of Evalued continuous functions C ( K , E) is distinguished and it,s strong dual is naturally isomorphic to Li (p)&EL where L i ( p ) = C ( K ) ' .
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