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Concerning the article "Bernstein, Allen R.; Robinson, Abraham. Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos. Pacific J. Math. 16 1966 421-431" I am interested in finding out the following : (1) who was the editor of the Pacific Journal of Mathematics at the time? as well as (2) who was the referee for the article? The latter is obviously the harder of the two questions but since this was nearly half a century ago perhaps such information can be made public. Are there books or articles that may shed light on either of these questions? Furthermore, (3) Since Halmos published his translation of the Bernstein-Robinson proof simultaneously in the same journal, he had to know about the upcoming publication of Bernstein-Robinson; how did he find out about it?

Note 1. I looked carefully through Dauben's biography of Robinson to see if he sheds any light on the hypothesis proposed by two respondents below that Halmos may have been a referee (among others) but Dauben doesn't shed any light on this. If anybody has information about this based on other books or personal recollections they are requested to contribute a comment or answer.

Note 2. One of the respondents below reproduced a page from Halmos' book where he claims that he first received the manuscript "early in 1966" (probably error of recollection). If that were the case, he certainly could not have been the referee since the manuscript by Bernstein and Robinson was originally submitted on 5 july 1964, and one can assume that the editor would not wait for over a year to send it out to a referee. Therefore it may be worth pointing out that Joseph Dauben documents a letter from Halmos to Robinson dated 19 june 1964 where Halmos acknowledges receipt of the manuscript. This can be found in Dauben's book on page 328, footnote 66.

Note 3. Several NSA experts have contacted me privately with educated guesses and it seems probable that the editor was Richard F. Arens and the referee Paul R. Halmos. Anyone who has additional information about this is requested to share it if possible.

Note 4. I was just informed by the editorial office of PJM that, while they are not certain, the editor for the submission was most likely Richard Arens.

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    $\begingroup$ I presume you want the answer to (1) in order to find out the answer to (2) --- which would be a breach of the confidentiality agreement between editor and referee. I don't think there is a statute of limitations for this confidentiality. $\endgroup$
    – Carlo Beenakker
    Commented Dec 7, 2015 at 12:04
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    $\begingroup$ No, that wasn't my plan at all since I sort of assumed that neither of them would be available for comment 50 years later :-) $\endgroup$
    – Mikhail Katz
    Commented Dec 7, 2015 at 18:33

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I can identify one individual who scrutinized the Bernstein-Robinson manuscript and established its validity before it was published in PJM:

Paul Halmos, I Want to be a Mathematician: An Automathography (1985).

So even if the identity of Halmos as referee cannot be established, he at least did the work of a referee.

Actually, Halmos did more than the work of a referee, the preprint he received from Robinson motivated him to build on it and he wrote his own contribution, which was published in PJM (immediately following the Bernstein-Robinson paper).

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  • $\begingroup$ Carlo, thanks for your comment. I think it may be unfair to Halmos to say that he published his paper "even slightly ahead of the Bernstein-Robinson paper". As I recall Halmos' paper appeared right after the Bernstein-Robinson one. $\endgroup$
    – Mikhail Katz
    Commented Dec 9, 2015 at 12:04
  • $\begingroup$ Also, I have the impression that the paper on quasitriangularity is a different paper (not the same as the Pacific Journal of Math paper). $\endgroup$
    – Mikhail Katz
    Commented Dec 9, 2015 at 12:06
  • $\begingroup$ Halmos, P. R. quasitriangular operators. Acta Sci. Math. (Szeged) 29 1968 283–293. $\endgroup$
    – Mikhail Katz
    Commented Dec 9, 2015 at 12:10
  • $\begingroup$ The passage from Halmos that you reproduced above contains a very surprising claim by Halmos. He claims that he received the manuscript from Robinson "early in 1966". In point of fact, he received the manuscript in june of 1964, i.e., two years earlier than what he is claiming here. $\endgroup$
    – Mikhail Katz
    Commented Dec 9, 2015 at 12:20
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    $\begingroup$ Halmos submitted his follow-up work on the Bernstein-Robinson paper to PJM on October 10, 1964, so he must have received their preprint earlier in 1964; the 1966 date that Halmos mentions when he looks back on these events two decades later must be an error of recollection. $\endgroup$
    – Carlo Beenakker
    Commented Dec 10, 2015 at 14:07
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(1) From the front of that issue of the PJM

PJM

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    $\begingroup$ Thanks,Gerald, this is very helpful (our library's subscription does not go that far back). I wonder which of them would have been a natural editor to handle the Bernstein-Robinson submission... $\endgroup$
    – Mikhail Katz
    Commented Dec 7, 2015 at 18:34
  • $\begingroup$ I got it on-line. Our library has an electronic subscription, which makes all the back issued available. $\endgroup$
    – Gerald Edgar
    Commented Dec 7, 2015 at 21:18
  • $\begingroup$ That's interesting actually. I wouldn't expect the electronic version to have the front cover information. They usually just provide electronic copies of each of the articles. Where did you find the title information exactly in the electronic edition? Was it part of one of the articles? The first one? $\endgroup$
    – Mikhail Katz
    Commented Dec 8, 2015 at 8:24
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    $\begingroup$ There were PDFs the individual articles, but also PDFs of whole issues. When you choose an issue, you get a listing of the articles on the right side of the page, but also at the top left you get "Download this issue". msp.org/pjm/1966/16-3/index.xhtml And it seems library subscription is not required to view these old issues. $\endgroup$
    – Gerald Edgar
    Commented Dec 8, 2015 at 15:19
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As a matter of pure speculation, a reasonable guess regarding a referee could be Smith and Halmos themselves (because they posed the conjecture) or perhaps Aronszajn because he had proved the compact case.

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