I'm reading a 1939 paper by the great and famous J. von Neumann, "On infinite direct products" (of vector spaces), available here http://www.numdam.org/item/?id=CM_1939__6__1_0, legally I presume.

What he calls the direct product is clearly what we understand today as a tensor product, while our understanding of the direct product is the full (possibly infinite) Cartesian product with some projections.

I'm interested what is the background for this, was this general usage in the dim and distant past, when did the terminology change and why?

(copied here from https://math.stackexchange.com/q/3857681)



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