John Rainwater

from Wikipedia, the free encyclopedia

John Rainwater is the name of a fictional mathematician or the pseudonym of a number of mathematicians, especially in the field of functional analysis , including Robert Phelps .

Between 1959 and 1990 around 16 essays, communications and seminar transcripts and, most recently, even collected works were published under his name at the University of Washington . They have appeared in major mathematics journals such as the Pacific Journal of Mathematics , the Duke Mathematical Journal, and the Proceedings of the American Mathematical Society .

The story of John Rainwater started as a student joke. In 1952, math student Nick Massey at the University of Washington accidentally got a blank registration card for an Introduction to Real Analysis course from math professor Maynard Arsove. He and his fellow student Sam Saunders submitted solutions to exercises under this name, which was only revealed when the first exams were due. Arsove took the joke calmly, even when he got an "exploding" fountain pen from Rainwater, and only remarked in front of the class that the only time he would see Rainwater would be in a barrel.

Years later, some math students and junior faculty at the University of Washington studying the American Mathematical Monthly's problem column came up with the idea of ​​submitting solutions under the pseudonym John Rainwater. When the editor of the journal, the Mathematical Association of America , offered Rainwater membership, the difficulty arose that two MAA members had to support it. The authors behind the pseudonym even managed to get the signature of Carl Allendoerfer , professor at the University of Washington and President of the MAA. Although he refused to participate in the joke himself, a privy secretary managed to get his signature on a pile of other papers for him to sign.

In 1959, the first scientific essay appeared under his name, written by Assistant Professor John Isbell , without this including any indication of the true identity, which was partly different in later papers under the name Rainwater. Isbell himself didn't mind (he also used two other pseudonyms for publications) and the pressure to publish for his career was not that high back then either. In addition to functional analysis, the essays were also, for example, from the areas of convex analysis, algebra and topology. At the end of the 1960s, the John Rainwater Seminar began at the University of Washington, initially dealing with functional analysis, and later with Fourier analysis and dynamic systems.

Rainwater's theorem gives necessary and sufficient conditions for the weak convergence of sequences in Banach spaces.

Phelps stated that his motivation for writing Rainwater's third paper was that he needed a folk theorem for his own work that had not yet been published but had been independently found by several mathematicians .

Fonts

  • Spaces whose finest uniformity is metric, Pacific J. Math. 9 (1959), 567-570 (by John Isbell, the most cited work by John Rainwater )
  • A note on projective resolutions, Proc. Amer. Math. Soc. 10 (1959), 734-735 (by John Isbell)
  • Weak convergence of bounded sequences, Proc. Amer. Math. Soc. 14 (1963), 999 (by Robert Phelps, a result of which became known as Rainwater's Theorem )
  • A remark on regular Banach algebras, Proc. Amer. Math. Soc. 18 (1967), 255-256 (by Irving Glicksberg )
  • On a renorming theorem of Klee, Unpublished note, 1968.
  • Local uniform convexity of Day's norm on c0 (G), Proc. Amer. Math. Soc. 22: 335-339 (1969). (the second most cited work by John Rainwater, written by a group of six authors)
  • Day's norm on c0 (G), Proc. of the Functional Analysis Week, Aarhus 8 (1969) 46-50. Matematisk Inst., Aarhus Univ., Aarhus (a follow-up on the previous work, written by Edgar Asplund for a conference in Aarhus)
  • A note on the preceding paper, Duke Math. J. 36 (1969), 779-800 (von Glicksberg, a total of four people were involved, but the result was relatively short so that it was published under Rainwater).
  • A characterization of certain dual unit balls, Rainwater Sem. Notes, 1970 (from Phelps).
  • Regular matrices with nowhere dense support, Proc. Amer. Math. Soc. 29 (1971), 361 (by John Isbell).
  • A non-reflexive Banach space has non-smooth third conjugate space, Rainwater Sem. Notes, 1972 (from Phelps).
  • A theorem of Ekeland and Lebourg on Frechet differentiability of convex functions on Banach Spaces, Rainwater Sem. Notes, 1976 (from Phelps).
  • Lindenstrauss spaces which are Asplund spaces, Rainwater Sem. Notes, 1976-77 (by Peter D. Morris).
  • Global dimension of fully bounded Noetherian rings, Comm. Algebra 15 (1987), 2143-2456 (a work on algebra by Ken Brown , Ken Goodearl, Toby Stafford , Bob Warfield)
  • Yet more on the differentiability of convex functions, Proc. Amer. Math. Soc. (1988), no. 3, 773-778 (by Isaak Namioka, Robert Phelps, they generalized a sentence by a doctoral student without exposing it, because they had mastered techniques that they did not yet know)
  • A class of null sets associated with convex functions on Banach spaces, Bull. Austral. Math. Soc. 42 (1990), no. 2, 315-322 (by Phelps and David Preiss ).
  • Problems / Solutions of John Rainwater (collection of solutions for the American Mathematical Monthly, first submitted by John Isbell in 1959, the last submitted by Phelps in 1994).
  • Collected Works of John Rainwater. The first 40 years (1959-1999), Department of Mathematics, University of Washington.

literature

  • Robert Phelps: John Rainwater, TopCom, Volume 7, 2002, online

Individual evidence

  1. ^ J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, Springer 1984, p. 155