{"id":4482,"date":"2013-02-17T13:41:42","date_gmt":"2013-02-17T21:41:42","guid":{"rendered":"http:\/\/experimentalmath.info\/blog\/?p=4482"},"modified":"2013-03-14T00:32:18","modified_gmt":"2013-03-14T08:32:18","slug":"in-memoriam-robert-r-phelps","status":"publish","type":"post","link":"https:\/\/experimentalmath.info\/blog\/2013\/02\/in-memoriam-robert-r-phelps\/","title":{"rendered":"In Memoriam: Robert R. Phelps (1926-2013)"},"content":{"rendered":"

Robert Ralph Phelps born March 22, 1926 died on January 4, 2013 aged 86<\/strong><\/p>\n

After an earlier career as a radio operator in the merchant marines,\u00a0Bob Phelps studied at the University of California in Los Angeles and then went on to completed a PhD from the University of\u00a0Washington in 1958 under the supervision of Victor Klee. His thesis\u00a0was entitled “Subreflexive normed linear spaces”. (A class of Banach spaces that disappeared when Bishop and Phelps showed all Banach spaces enjoyed this very important property!) \u00a0After\u00a0spending two years at the Institute of Advanced Study in Princeton\u00a0and a further two years at the University of California in Berkeley,\u00a0he obtained a position in 1962 at the University of Washington in\u00a0Seattle where he continued to teach until his retirement, becoming\u00a0Emeritus in 1996. The academic year of 1969-70 was spent at the\u00a0Pierre-and-Marie-Curie University (Jussieu Campus, known as `Paris VI’) on the\u00a0invitation of Gustave Choquet with whom he enjoyed a\u00a0friendly relationship.<\/p>\n

\"phelps\"<\/a>

Bob Phelps circa 1978<\/p><\/div>\n

Bob Phelps was an outstanding analyst; leaving behind a legacy of\u00a0results that continue to have a strong impact in functional analysis\u00a0and the theory of Banach spaces, including optimization. Besides publishing more than 70 papers\u00a0he authored three highly influential books and sets of lecture notes:<\/p>\n

    \n
  1. Lectures on Choquet’s theorem,<\/em> (Springer 1966, 2nd edition<\/a> 2001) which provides an easily penetrated\u00a0account of the theory of integral representations of convex sets. In\u00a0the most recent edition he considered applications to approximation\u00a0theory; including, for instance, Korovkin’s theorem and its\u00a0extension due to Shashkin. Each of the us recall studying from this\u00a0book as students and one (Thera) took part in Gustave Choquet’s the course and\u00a0seminar in which the analysis had been initiated.<\/li>\n
  2. Lectures on the Differentiability of convex functions on Banach spaces<\/em> \u00a0(1977-78),\u00a0<\/em>which in its initial version was working notes from the course he\u00a0had given at University College London while visiting David Larman.<\/li>\n
  3. Convex functions, monotone operators and differentiability<\/em> (Springer 1989, 2nd edition<\/a>\u00a01993), has become\u00a0a highly cited classic. In the second edition he integrated recent\u00a0results due to D. Preiss, R. Haydon, J.M. Borwein, S. Fitzpatrick,\u00a0P. Kenderov and new work of S. Simons.\u00a0This book which treats,\u00a0among other things, the variational principles of Ekeland, Borwein-Preiss, Deville,\u00a0Godefroy and Zizler, has provided \u00a0many valuable insights for our work\u00a0as researchers.<\/li>\n<\/ol>\n

    Bob collaborated with many eminent mathematicians: Isaac Namioka (a\u00a0long standing colleague at the University of Washington), Joram\u00a0Lindenstrauss, David Preiss, Simon Fitzpatrick (who was his\u00a0student), Bernardo Cascales, Jose Orihuela, Gilles Godefroy, Frank\u00a0Bonsall, David Larman, Stephen Simons and Jean-Baptiste\u00a0Hiriart-Urruty. With the last of these he published an article in\u00a0the Journal of Functional Analysis establishing a general formula\u00a0for the subdifferential of the sum of two convex semi-continuous\u00a0functions without any additional conditions using only \u00a0epsilon-subdifferentials. A result important to work by two of\u00a0us (Borwein, Thera).<\/p>\n

    The best known result of Bob Phelps is probably the celebrated\u00a0Bishop-Phelps theorem <\/em>obtained in collaboration with Errett Bishop,\u00a0a student of Paul Halmos, better known for his “constructivist”\u00a0stance.\u00a0\u00a0<\/em>On \u00a0Bob Phelps’ website one can find an article\u00a0<\/a>explaining the genesis of this result which quickly became one of\u00a0the corner stones of Banach space theory. The theorem establishes\u00a0that the support functionals to a closed convex nonempty\u00a0bounded set C in a Banach space E are dense in the cone of\u00a0linear functionals bounded from below on $C$} has proved basic to\u00a0many areas including the theory of optimization. And, has been the\u00a0source of several celebrated generalizations, for example, the\u00a0theorem of Brondsted & Rockafellar, which shows that if\u00a0f is a lower semi-continuous convex extended-real-valued function\u00a0on a real Banach space E, then the set of points where the subdifferential of f is nonempty is dense in the domain of the\u00a0<\/em>functional (the set of points where the function is finite).<\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/p>\n

    In 1986, Phelps travelled to Montreal to give the opening lecture in in a workshop at CRM on differentiability of Lipschitz functions organized by John Giles and one of us (Borwein). In those days Americans frequently travelled to Canada with little ID. When Bob showed his driver’s license he was sent into the office of the head of immigration at Montreal airport. The man asked what he was doing. Bob explained and showed the meeting program. The official noted Bob’s title was “On the Bishop-Phelps theorem.” He said “Oh, you have a theorem named after you, is it any good?” Bob modestly replied that it had proven useful, at which point the man stamped an entry visa on the program and said “Welcome to Canada.” Bob thanked him and asked why he had been stopped. The reply: “We meet the most interesting people this way.”<\/p><\/blockquote>\n

    <\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em>The Phelps extremization principle applied to the epigraph of a\u00a0lower semi-continuous function allows us to derive an elegant proof\u00a0of the Ekeland variational principle in Banach space. This intuition yields many more recent\u00a0variational\u00a0principles.<\/p>\n

    Bob was an active member of the Department of Mathematics at the\u00a0University of Washington. He served as Department Chair for several\u00a0years and together with his wife Elaine, who was a linguist,\u00a0endowed the Robert R. and Elaine F. Phelps Professorship<\/em>.\u00a0Bob Phelps was a convinced atheist and, rare for an American, almost\u00a0militant in his views. He was also an accomplished sportsman; a\u00a0runner, marathon walker and mountaineer par excellent. He ran every\u00a0day, rain-hail or shine and, as one of us (Thera) remembers from aconference organized in Bulgaria, at a pace that no untrained\u00a0colleague could have maintained.<\/p>\n

    At the University of Washington Bob founded and lead a regular\u00a0research seminar known as the Rainwater Seminar<\/em> \u00a0(named\u00a0after Mount Rainier, a snow draped dormant volcano iconic of\u00a0Washington State and visible from his office, or was it named to\u00a0reflect the nature of Seattle’s inclement climate). In deference to\u00a0the Australian accent, while one of us (Sims) and several other\u00a0Australians were visiting in the late seventies Bob in keeping with\u00a0his wry sense of humour changed the name to “Rinewater”. Many of the\u00a0significant results in functional analysis from the latter part of\u00a0the 20th century were first announced at these seminars and results\u00a0emerging from discussions during and after the seminar were often\u00a0published under the name of \u00a0“John Rainwater”.<\/p>\n

    We close with an amusing account that Bob passed on to J.-B.\u00a0Hiriart-Urruty.<\/p>\n

    In the sixties: he had been invited by G. Choquet toa rather posh restaurant in Paris for dinner where he was served an exquisite piece of meat, too large for him to quite finish. He\u00a0considered taking it home to have later, and thought to himself that\u00a0back in the US he would simply have asked for a “Doggy Bag”, but\u00a0knew that in Paris taking away the remainders of a meal was a no-no,\u00a0as it is even today. Never mind, he gingerly calls a waiter and\u00a0tells him in a whisper that he would like to take the meat on his\u00a0plate … for his dog. The waiter swiftly removes the plate saying\u00a0in a confident tone: “Sir, I have something much better for your\u00a0dog, I’ll bring you some bones!”.<\/p><\/blockquote>\n

    <\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em><\/em>With the passing of Bob Phelps we lose an outstanding mathematician,\u00a0sportsman and a modest and deeply humanistic colleague. He will be much missed.<\/p>\n

    Michel Thera, Brailey Sims and Jon Borwein<\/p>\n

    Post Script.<\/strong> \u00a0We have received various notes from former colleagues, friends and students of Bob. \u00a0Stephen Simons wrote:<\/p>\n

    I have a little story that tells you what Bob did after retirement (using the skills he developed during the war as a radio operator). \u00a0 A few years ago, I visited him in Seattle and I noticed some old clothes and other assorted bits of junk strewed over the back seat of his car. \u00a0 He told me that this junk was actually covering more than $500 of sophisticated communications equipment. \u00a0 He explained that he had a position in the local organization that was prepared for a (terrorist, seismic or volcanic) disaster.<\/p>\n

    As you say, he will be missed.<\/p>\n

    On March 3, 2013 this obituary<\/a>\u00a0appeared in the Seattle Times.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"

    Robert Ralph Phelps born March 22, 1926 died on January 4, 2013 aged 86<\/p>\n

    After an earlier career as a radio operator in the merchant marines, Bob Phelps studied at the University of California in Los Angeles and then went on to completed a PhD from the University of Washington in 1958 under the supervision of Victor Klee. His thesis was entitled “Subreflexive normed linear spaces”. (A class of Banach spaces that disappeared when Bishop and Phelps showed all Banach spaces enjoyed this very important property!) After spending two years at the Institute of Advanced Study in Princeton and a <\/p>\n

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