Bob Doran
Program Affiliations
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
Mathematical Reviews of Books and Research Papers
Presently, Doran has written 567 reviews (and counting) including 23 major book reviews of which 5 are “Featured Reviews”. All reviews are available on the AMS MathSci web page. Doran also reviews for the Bulletin of the AMS amd Zentralblatt.
Legendary MIT Professor Gian Carlo Rota wrote the following review of one of Doran’s own books, coauthored with TCU colleague Victor Belfi, titled: Characterizations of C*-algebras: The Gelfand-Naimark Theorems, published in 1986 by Marcel-Dekker:
Review: “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, Advances in Mathematics, Vol. 62 (1986), 101-102
Two Books
Doran has published 16 books (see Wikipedia). His first one, “Approximate Identities and Factorization in Banach Modules” (Springer-Verlag), 1979, coauthored with Josef Wichmann, is based on Doran’s TCU graduate lectures. A massive two-volume project, with J. M. G. Fell, titled “Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles”, vol. 1 and vol. 2 (Academic Press), with total of 1,486 pages and took eight years (1980–1988) to complete. This is Doran’s best work!
One Short Research Paper: The Kaplansky Problem Solved
In 1949 Irving Kaplansky, distinguished University of Chicago Professor, asked if one adjoined a unit to a symmetric Banach *-algebra, was the result symmetric? In 1959, it was shown to be true by P. Civin and B. Yood. New question: “What about arbitrary symmetric *-algebras?” This question remained open for the next 12 years and became famous as the “Kaplansky Problem”. In 1971, after many years of effort, Doran finally showed, in a few lines, that again the answer is “yes” (see Bull. of the London Math. Soc. 4 (1972), 25–26). Professor Kaplansky wrote to Doran: “Thanks for demolishing the ridiculous contortions of all your predecessors––I enjoyed the proof!”
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
Last Updated: September 23, 2026