After completing his Ph.D., Ringrose was appointed a lecturer in mathematics at King's College of the University of Newcastle-upon-Tyne in 1957. He remained in Newcastle until 1961 when he returned to Cambridge as a lecturer in mathematics. He was also elected a fellow of his old College, St John's College, Cambridge. He remained at Cambridge for two years then, in 1963, Ringrose returned to Newcastle where he was appointed a senior lecturer in mathematics.
In 1964 he was appointed to the chair of Pure Mathematics at the University of Newcastle-upon-Tyne and he held this post until he retired in 1993. On his retiral he became professor emeritus at Newcastle. He also served as Pro-Vice-Chancellor at the University of Newcastle-upon-Tyne from 1983 until 1988.
Ringrose is a leading world expert on non-self-adjoint operators and operator algebras. He has written on operators of Volterra-type, compact linear operators, the Neumann series of integral operators, algebras of operators, automorphisms and derivations of operator algebras, and the cohomology of operator algebras.
He has written a number of influential texts including Compact non-self-adjoint operators (1971) and, with R V Kadison, Fundamentals of the theory of operator algebras in four volumes published in 1983, 1986, 1991 and 1992. The first of these volumes is an elementary approach to the theory of C*-algebras and von Neumann algebras. The authors state in the preface that their:-
... primary goal is to teach the subject and lead the reader to the point where the vast recent literature, both in the subject proper and in its many applications, becomes accessible.The second volume treats advanced topics which Ringrose and Kadison consider to be fundamental for an understanding of current research in operator algebras. R S Doran, a reviewer of the text, writes that:-
The book [is] written by two eminent mathematicians each of whom has made major contributions to the theory of operator algebras.He concludes the review saying that:-
...the authors have presented [the material] in a fresh and attractive way which conveys the spirit and beauty of the subject. They are to be commended for writing a beautiful book which, in the reviewer's opinion, fulfills all of the promises made in the preface.These two volumes contain an outstanding collection of exercises which in many cases lead the reader to prove some further major results by skillfully breaking them down into manageable parts. The third and fourth volumes contain the solutions to the exercises. R S Doran says the authors' solutions:-
... which were developed from scratch specifically for this volume, are models of clarity and efficiency, reflecting their vast experience and insight into the subject.The Royal Society of London elected Ringrose as a fellow in 1977 and he has also been elected a fellow of the Royal Society of Edinburgh. He has served the London Mathematical Society in many different ways including holding the position of president of the Society from 1992 to 1994.
Article by: J J O'Connor and E F Robertson