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Given two Hilbert spaces $H_1$ and $H_2$, together with two bounded linear maps $L_i \in \mathcal{B}(H_i)$, for $i=1,2$. What is the most easiest way to explain that the product $L_1 \times L_2$ extends to a bounded linear operator on the tensor product of Hilbert spaces $H_1 \otimes H_2$?

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