American mathematician, best known for his work on operator theory and operator algebras. Among his best-known contributions to science is a 1977 paper with Lawrence G. Brown and Peter A. Fillmore (BDF theory), which introduced techniques from algebraic topology into the theory of operator algebras. In addition to BDF theory, two other influential theories bear his names: Douglas algebra and Cowen-Douglas operators. In recent decades, he is a prominent advocator of multivariable operator theory. His coauthored book with V. Paulsen, Hilbert modules over function algebras, introduced an analytic framework for studying commuting operator tuples. Douglas-Arveson conjecture is a well-known unsolved problem in this field.
Douglas was an undergraduate at the Illinois Institute of Technology, and received his PhD in 1962 from Louisiana State University as a student of Pasquale Porcelli. He was at the University of Michigan until 1969, when he moved to the State University of New York at Stony Brook. Beginning in 1986 he moved into university administration, eventually becoming Vice Provost at Stony Brook in 1990, and Provost at Texas A&M University from 1996 until 2002. He was a Distinguished Professor in the Department of Mathematics at Texas A&M.
Douglas directed 23 PhD students, some of whom became renowned mathematicians, and his book Banach Algebra Techniques in Operator Theory in the series Graduate Texts in Mathematics is one of the classics in operator theory.
In 2012 he became a fellow of the American Mathematical Society.
He has three children, including Michael R. Douglas, a noted string theorist. He died on 27 February 2018, aged 79.
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