Abstract.We show that if A" is a -2oo -space with the Dieudonné property and y is a Banach space not containing l\ , then any operator T: X®e Y -> Z , where Z is a weakly sequentially complete Banach space, is weakly compact. Some other results of the same kind are obtained.Let A be a Jz^-space (see [1] for this notion and some useful results on Jz^-spaces) and Y be a Banach space not containing l\ . We consider the injective tensor product X ®£ Y (see [3]), and we investigate the following problem: when is any operator T : X
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