Robert Phelps

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Robert R. Phelps

Robert Ralph Phelps (born March 22, 1926 in San Bernardino , California ; † January 4, 2013 ) was an American mathematician who is known for his contributions to analysis , in particular functional analysis and measure theory . From 1962 he was professor of mathematics at the University of Washington .

Life

Phelps studied mathematics at the University of California, Los Angeles and graduated in 1954 with a bachelor's degree . He wrote his dissertation in 1958 at the University of Washington on subreflective Banach spaces , supervised by Victor Klee . 1958/59 he was an instructor at Princeton University and from 1958 to 1960 at the Institute for Advanced Study . From 1960 to 1962 he did research at the University of California, Berkeley . In 1962 he became an assistant professor at the University of Washington with a full professorship from 1966. He taught as a visiting professor at the University of Paris from 1969 to 1970 and at University College London from 1977 to 1978.

Together with Errett Bishop , Phelps proved the Bishop-Phelps theorem about convexity in Banach spaces and in particular the so-called Bishop-Phelps theorem (in English technical literature) , which is an essential result of functional analysis and applications in operator calculus , harmonic analysis , the Choquet -Theory and the calculus of variations has.

Phelps wrote some books, some of which were republished. 1966 was his book Lectures on Choquet's theorem ( Lectures on the set of Choquet ), the first book to the theory of integral Representationen said. His works have been translated into Russian and other languages. A revised and expanded version of the Lectures on Choquet's theorem was published again in 2002. Like other mathematicians, he published in the field of function analysis under the pseudonym John Rainwater . It started as a student joke in 1952 and resulted in a number of academic publications under that name. Phelps himself presented the story of "John Rainwater" in an essay.

Phelps worked in the field of nonlinear analysis, particularly in a monograph on differentiability and Banach space theory. In his foreword Phelps pointed out the requirement “background in functional analysis”: “ the main rule is the separation theorem (aka [also known as] the Hahn – Banach theorem ): Like the standard advice given in mountaineering classes (concerning the all -important bowline for tying oneself into the end of the climbing rope), you should be able to employ it using only one hand while standing blindfolded in a cold shower ”( Phelps 1991 , German:“ The main rule is the separation theorem (also Hahn – Banach theorem). You should be able to apply them like the standard rule in mountaineering training (to rope up, also with one hand blindfolded under a cold shower ”) Phelps was a good mountaineer and used metaphors from this area to illustrate mathematical relationships .

In 2012 he became a Fellow of the American Mathematical Society . He was married to Elaine Phelps.

selected Writings

  • Errett Bishop, RR Phelps: A proof that every Banach space is subreflexive . In: Bulletin of the American Mathematical Society . 67, 1961, pp. 97-98.
  • Robert R. Phelps: Convex functions, monotone operators and differentiability  (= Lecture Notes in Mathematics), Second edition of 1989. Edition, Volume 1364, Springer-Verlag, Berlin 1993, ISBN 3-540-56715-1 , pp. Xii + 117.
  • Robert R. Phelps: Lectures on Choquet's theorem. Van Nostrand 1966, 2nd edition. Lecture Notes in Mathematics 1757, Springer Verlag, 2001, ISBN 3-540-41834-2 .
  • I. Namioka, Robert R. Phelps: Banach spaces which are Asplund spaces . In: Duke Math J. . 42, No. 4, 1975, pp. 735-750. ISSN  0012-7094 .

literature

Web links

Individual evidence

  1. ^ Career data American Men and Women of Science , Thomson Gale 2004.
  2. ^ A b c d Robert R. "Bob" Phelps / Obituary , The Seattle Times. March 3, 2013. 
  3. ^ HE Lacey: Review of Gustave Choquet's (1969) Lectures on analysis , Volume III: Infinite dimensional measures and problem solutions . In: Mathematical Reviews . September.
  4. ↑ L. Azimov, AJ Ellis :: Convexity theory and its applications in functional analysis  (= London Mathematical Society Monographs), Vol 16, Academic Press, [Harcourt Brace Jovanovich, Publishers], London / New York 1980, ISBN 0-12- 065340-0 , p. X + 266.
  5. ↑ Richard D. Bourgin: Geometric aspects of convex sets with the Radon-Nikodým property  (= Lecture Notes in Mathematics), Volume 993. Springer-Verlag, Berlin 1983, ISBN 3-540-12296-6 , pp. Xii + 474.
  6. ^ Robert R. Phelps: Biography of John Rainwater . In: Topological Commentary . 7, No. 2, 2002.
  7. ^ P. Iii of the 1989 edition Phelps (1991).
  8. ^ List of Fellows of the American Mathematical Society , accessed May 5, 2013
  9. ↑ Peter Gritzmann, Bernd Sturmfels: Victor L. Klee 1925–2007 ( English , PDF; 144 kB) American Mathematical Society. Pp. 467-473. April 2008. Retrieved October 18, 2013.
personal data
SURNAME Phelps, Robert
ALTERNATIVE NAMES Phelps, Robert Ralph (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH March 22, 1926
PLACE OF BIRTH San Bernardino , California
DATE OF DEATH 4th January 2013