Does anyone know if there exists an English translation of von Neumann's early work in operator theory, in particular the paper Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren?

The full citation is

von Neumann, J., Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren., Math. Ann. 102, 370-427 (1929). ZBL55.0825.02. EuDML (link to free version) .

If not, are there any expository works in English from around that time period covering von Neumann's work, maybe say pre-1950?

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    $\begingroup$ no english translation is listed in the bibliography $\endgroup$ Commented Apr 8, 2021 at 7:00
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    $\begingroup$ Try Google Translate. This is what I did when I ran out of options. It's not ideal but it's a math paper and the translation will give you enough hints to figure out what is going on. One positive thing about this is that you will read the paper much more carefully than any paper in language you are fluent in. $\endgroup$ Commented Apr 8, 2021 at 10:52
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    $\begingroup$ Or DeepL, it's actually quite reasonable. $\endgroup$
    – David Roberts
    Commented Apr 10, 2021 at 10:31

1 Answer 1


If I am not mistaken this has been done by R. Lakshminarayanan and you can find it in

Bródy, F. (ed.); Vámos, T. (ed.), The Neumann compendium, World Scientific Series in 20th Century Mathematics. 1. Singapore: World Scientific. lix, 699 p. (1995). ZBL0829.01029.

part/chapter 3, pages 182-243: Algebra of Functional Operations and Theory of Normal Operators. See on Google Books.


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