He was an undergraduate at the Illinois Institute of Technology, and received his Ph.D. in 1962 from Louisiana State University as a student of Pasquale Porcelli.

He is survived by three children, including Michael R. Douglas, a noted string theorist.

This work was an important precursor to noncommutative geometry as later developed by Alain Connes among others.

His coauthored book with Vern Paulsen "Hilbert modules over function algebras" introduced an analytic framework for studying commuting operator tuples.

Douglas directed 23 Ph.D 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.