Robert Phelps

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

Life

Phelps studied mathematics at the University of California, Los Angeles and graduated in 1954 as a bachelor's degree. He wrote his dissertation in 1958 at the University of Washington on subreflexive Banach spaces, supervised by Victor Klee. 1958/59 he was instructor at Princeton University, and from 1958 to 1960 at the Institute for Advanced Study. 1960 to 1962 he conducted research at the University of California, Berkeley. In 1962, he was 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 until 1978.

With Errett Bishop Phelps proved the Bishop - Phelps theorem, an important result of the functional analysis, with applications in operational calculus, harmonic analysis, Choquet theory and calculus of variations.

Phelps wrote several books that have been published in part again. 1966 was his book Lectures on Choquet 's theorem ( Lectures on the theorem of Choquet ) the first book that explained the theory of integral Representationen. His works have been translated into Russian and other languages ​​. A revised and expanded version of the Lectures on Choquet 's theorem was published in 2002. He also published under the pseudonym of John Rainwater.

Phelps worked in the field of non-linear analysis, especially in a monograph on differentiability and Banach space theory. In his preface Phelps pointed to the requirement "background in functional analysis " out, " 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). which you should be able to use as the default rule in the mountaineer training ( to rush out ), even with one hand while blindfolded under a cold shower " ) Phelps was a good climber 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 did 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, second edition of 1989, 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: Banach spaces are Asplund spaces Which. In: Duke Math J. 42, No. 4, 1975, pp. 735-750.