1
$\begingroup$

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)

Improve this question
$\endgroup$
2
  • 2
    $\begingroup$ This use of the term “direct product” for tensor products goes back to Murray and von Neumann in 1936. See my previous question on the notation for tensor products hsm.stackexchange.com/questions/7018/… and the last paragraph of Section 1 in kconrad.math.uconn.edu/blurbs/linmultialg/tensorprod.pdf. $\endgroup$
    – KCd
    Commented Jan 25, 2021 at 5:29
  • $\begingroup$ Van der Waerden uses "direct product" for tensor product of algebras in Moderne Algebra (1930), §67. $\endgroup$
    – Conifold
    Commented Nov 21, 2021 at 6:12

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.