Bob Doran

Education

• B.A. University of Iowa, (1962); M.S. (1964) 
• M.S. University of Washington (1967)
• Ph.D. University of Washington, (1968)

A Personal Note of Thanks to the Rusty and Deedie Potter Rose Family

I had the great privilege teaching at TCU for 47 years (1969-2016), twenty-one of them as Math Chair (1990-2011) and also twenty-one years as the inaugural Potter Professor (1995-2016). Although now formally retired, I still hold a graduate faculty appointment through 2028. My TCU colleagues have been immensely supportive of the department over the years. Of course, math is “beyond amazing” to all of us who love it and have experienced its power and awesome beauty (and, to put the cherry on top, we get to actually teach it to our students!). With these thoughts in mind and, as the initial holder of the Potter Professorship, I and the TCU mathematics faculty graciously want to express (once again) to the entire Rusty & Deedie Potter Rose family our deepest heartfelt “thanks” for the generous gift to the Department of Mathematics in 1995. This wonderful gift has had a profound impact on the lives of everyone it has touched over the past thirty-plus years! Rusty made it clear to me that he loved mathematics!

 ~Bob Doran

Areas of Focus

Operator Algebras, C*-Algebras, Banach *- Algebras & Fell Bundles, Harmonic Analysis, Representations of Locally Compact Groups, Banach Modules, Approximate Identities, Functional Analysis

Selected Publications, Research and Teaching

• Curriculum Vitae
• Doran/Wikipedia
• Doran/Ph.D. Students
• Doran/Institute for Advanced Study, Princeton AMIAS
• Doran/Math Institute Oxford University
• Doran/Massachusetts Institute of Technology
• Doran & A. Ramsay/George Mackey 1916 – 2006
• Doran/Dieudonné: History of Functional Analysis

Doran's Reviews & Books and a Solution to a Problem of Kaplansky 

Math Reviews

Doran has written 568 mathematical reviews to date that include 23 major math books, 5 of which were selected as “Featured Reviews.” All reviews are available on the AMS MathSciNet Web Page. Doran has also written reviews for the Bulletin of the AMS and Zentralblatt. For example, see Doran’s review of Professor Jean Dieudonné’s “History of functional analysis”  in Bull. AMS, 7 (1982), No. 2, 403-409. This review is available on-line or see the link above. 

     On the other hand, legendary MIT Professor Gian-Carlo Rota, wrote the following positive review of one of Doran’s own books (coauthored with colleague Victor Belfi) written in 1986 titled “Characterizations of C*-algebras: The Gelfand-Naimark Theorems”:

REVIEW (Advances in Math., 62 (1986), 101):“This is probably the best-written treatise of functional analysis since Riesz and Nagy’s famous textbook of the fifties.  It is also the first comprehensive book to give full billing to Stinespring’s beautiful—and sometimes unjustly rejected—theorem.  Few mathematicians nowadays take the trouble of writing with the clarity and elegance of Doran and Belfi, and their lead should be followed by everyone who can write mathematics.”      — Gian-Carlo Rota MIT (1986)

Two Selected Book Projects

Doran has published 16 books to date (see Wikipedia above). His first, “Approximate Identities and Factorization in Banach Modules”(Springer), 1979, written with Josef Wichmann, was based on Doran’s graduate-level TCU Banach algebra lectures.

      Doran’s contribution to the massive 2-volume, eight year (1980–1988) book project, coauthored with his advisor, J.M.G. Fell, titled “Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles,” vols. 1 & 2 (Academic Press), 1988, totaling 1,486 pages, is considered his most important and significant work as shown by the numerous citations and deep non-trivial research papers it has produced.  

A Very Short Research Paper:  A Solution to the The Kaplansky Problem

In 1949, University of Chicago distinguished professor Irving Kaplansky asked in the Duke Mathematics Journal if one adjoined a unit to a symmetric Banach *-algebra, is the result symmetric?  Ten years later, P. Civin & B. Yood gave a positive solution. New Question: “What about arbitrary symmetric *-algebras?” This question remained open for 12 more years and became famously known as the “Kaplansky Problem.”  In 1972, after years of effort, Doran showed, in a few cleaver lines, once again the answer is “yes” (Bull. of the London Math. Soc. 4 (1972), 25–26). Professor Kaplansky wrote to Doran on University of Chicago letterhead: “Thanks for demolishing the ridiculous contortions of your predecessors––I enjoyed the proof!”   ––Irving Kaplansky

Selected Honors and Awards

• United States CASE-CARNEGIE National Gold Medalist & Professor of the Year 1989
• Texas CASE-CARNEGIE Professor of the Year 1989
• Texas Inaugural MAA (Math. Assoc. of America) Professor of the Year 1992
• Piper Professor Faculty Award, Minnie Stevens Piper Foundation 1989
• TCU Chancellor’s Award for Distinguished Teaching 1988
• TCU Honors Professor of the Year, Honors College 1993
• Phi Beta Kappa Liberal Arts Honor Society
• Burlington Northern Award for Distinguished Teaching 1986
• AMS Fellow Nomination by four distinguished AMS Fellows 2016 (R.A. Gangolli (PhD MIT); C.C. Moore (PhD Harvard); G.A. Folland (PhD Princeton); V.S. Varadarjan (PhD Calcutta)

Bob & Shirley Doran enjoying a TCU Baseball Game