**Richard Kadison**was known to his friends and colleagues as Dick. His parents were David Edward Kadison (29 May 1895 - 26 August 1974) and Rae Siegel (23 April 1900 - 27 August 1988). David Kadison had been born in New York to parents Jacob L and Sophie Kadushin. He became a salesman and later an architect in the building industry. Rae Siegel was born in Russia to Russian parents Israel Siegel and Lena Weisberg. The Siegel family emigrated to the United States in 1902. David and Rae Kadison were married in the Bronx, New York, on 22 September 1924. David Kadison had changed the spelling of his name from Kadushin to Kadison before his marriage; he was still David Kadushin in the 1920 census.

Richard Kadison attended the Bronx High School of Science, graduating in 1942. Robert Osserman (1926-2011), who became a professor of mathematics at Stanford University, said in the interview [7]:-

Kadson studied at the City College of New York but, because of World War II, served in the US Navy before completing his education. He served on various vessels, for example he was in France and returned to New York on the Sea Tiger as a junior 3rd mate, arriving on the 3 August 1945. He was then engaged in Baltimore as a 3rd mate on 9 November 1945 serving on the Henry St George Tucker. His record for the Sea Tiger gives his height as 5' 8" and his weight as 162 lbs (and 169 lbs on the second ship). After completing his war service, he returned to his studies undertaking research at the University of Chicago with Marshal Harvey Stone as his thesis advisor.I was very lucky with schools. I grew up in New York City which had some wonderful public high schools, and just at the time I was ready to think about where to go they started two new ones - the first specialty high schools. One was the High School of Music and Art, the other was the Bronx High School of Science. Both of them were free public high schools, but they required an examination to get in and admission was on a competitive basis. I was a member of the first full graduating class of the Bronx High School of Science and I had some wonderful teachers, as well as terrific fellow students. One of my classmates(who happened coincidentally to live in the same apartment house in Manhattan that I did)was Richard Kadison, who became a well-known mathematician ...

Not only did Kadison excel with his mathematical studies, but he also was a remarkable gymnast, being a member of the University of Chicago gymnastic team. Paul Wilson writes [9]:-

Kadison graduated with a Ph.D. from the University of Chicago in 1950 after writing his 108-page thesisIn the early1960s, my father told me of a brilliant gymnast at the University of Chicago. My father started at Chicago in1948, after he returned from the war, and he completed his MBA in1955. My father was a gymnast, a specialist in the flying rings, and he told me of Dick Kadison, a genius with the still rings.

*A Unified Representation Theory for Topological Algebra.*After graduating, he was a National Research Fellow at the Institute for Advanced Study at Princeton, being a member from September 1950 until June 1952. He published five papers in 1951 and four in 1952.

For a list of publications by Kadison, see THIS LINK.

Two of the 1951 papers are joint works by Kadison and Bent Fuglede who, after graduating with a D.Phil. from the University of Copenhagen in 1948, was at the Institute for Advanced Study from August 1950 until April 1951.

Kadison was appointed assistant professor at Columbia University, New York, in 1952. He was a Fulbright Research Fellow during 1954-55, promoted to associate Professor in 1956, an Alfred P Sloan Research Fellow from 1958-62, and a full professor in 1960. He was a Fulbright Research Fellow in Copenhagen (1954-55). On 5 June 1956 he married Karen M Holm (born in Sioux City, Iowa, on 23 December 1931); they had one son Lars David Kadison who was born on 24 February 1958. Lars Kadison went on to become a mathematician being awarded a Ph.D. from the University of California, Berkeley, in 1989 for his thesis* Cyclic Homology of Extension Algebras with Application to Matrix Algebras, Algebraic K-Theory and Nest Algebras of Operators*.

During his time at Columbia University, Kadison made trips to Denmark with his family. For example in the summer of 1960 Kadison, his wife and two-year old son, went to Denmark. They returned on 12 September, flying from Copenhagen to New York on flight SK903.

An important aspect of Kadison's work at Columbia was the Ph.D. students he attracted and advised. We should make special mention of Richard Kenneth Lashof (*Topological Group Extensions and Lie Algebras of Locally Compact Groups*, 1954); James G Glimm (*On a Certain Class of Operator Algebras*, 1959); Marc Aristide Rieffel (*A Characterization of Commutative Group Algebras and Measure Algebras*, 1963); Erling Størmer (*Point Measures in the Two-Sided Non-Commutative Integration Theory*, 1963); and Laurence Terrell Gardner, Jr. (*On Isomorphisms of C*-Algebras*, 1964). These students all became university professors and advised their own Ph.D. students.

Kadison left Columbia University in 1964 to take up the Gustave C Kuemmerle chair of mathematics at the University of Pennsylvania. *The Columbia Daily Spectator* reported on 28 April 1964 [4]:-

The University of Pennsylvania had gone to great lengths to attract Kadison to come [6]:-Richard V Kadison, professor of mathematics, will leave Columbia at the end of the term to assume the Gustave C Kuemmerle chair in mathematics at the University of Pennsylvania, President Gaylord P Harnwell of Pennsylvania has announced. His departure adds to an unusually large turnover in the mathematics department. Professor Kadison,38, is a leading expert in the field of functional analysis. He became a full professor at Columbia in1960. Appointed assistant professor in1952, he was a Fulbright Research Fellow during1954-55and an Alfred P. Sloan Research Fellow from1958-62. He is in France for the1964spring semester. Professor Ellis R Kolchin, chairman of the department, expressed some surprise at Professor Kadison's decision to leave. He noted, "we mustn't pretend that we're not hurt by the departure of Kadison."

[Kadison did a remarkable job at the University of Pennsylvania, both in the books and papers he produced, and in the mathematicians and students he attracted [6]:-He]was attracted to Penn in1964as part of the mid-sixties modernization and build-up of Penn's Mathematics Department undertaken by the then Provost David Goddard and the then Chairman Oscar Goldman. Indeed, Provost Goddard gave up his own chair(the Gustave C Kuemmerle Chair)to help attract Kadison to Penn. Dick held the Kuemmerle chair for the rest of his life.

Along with John Ringrose, Kadison published the two volume bookAt Penn, he was instrumental in building a world famous group in his own area of mathematics(functional analysis and operator theory); in the seventies, this was a great attraction for people to visit Penn's Math Department. The area of operator theory is not only pure mathematics, it has deep connections to quantum mechanics and quantum field theory, to probability theory as well as to other areas of mathematics. Dick worked tirelessly at the subject and its applications, he was known world-wide; he was an international mathematician.

*Fundamentals of the Theory of Operator Algebras*with volume 1, subtitled

*Elementary Theory,*appearing in 1983 and volume 2, subtitled

*Advanced Theory,*appearing in 1986. This work has become a classic and was reprinted in 1997. The two authors produced a further two volumes, the first being volume 3 subtitled

*Special topics. Elementary theory - an exercise approach*published in 1991 and volume 4 subtitled

*Special topics. Advanced theory - an exercise approach*appearing in 1992. Robert S Doran writes in a review of Volume 1:-

Nick Lord writes in [5]:-The book under review, written by two eminent mathematicians each of whom has made major contributions to the theory of operator algebras, is the first of two volumes devoted to a "textbook" treatment of the theory of C*-algebras and von Neumann algebras. The authors' purpose is clearly stated in the first paragraph of the preface: "[Our]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." This point of view is to be contrasted with the many(excellent)existing books on the subject, which are primarily directed toward the research mathematician, or exist to provide background on operator algebras for applications in theoretical physics. ... Although the material in this first volume is standard and well known to experts, the authors have presented it 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, fulfils all of the promises made in the preface.

Over his career, Kadison attended many conferences and published in the conference proceedings. In fact our list of his publications contains sixteen papers published in conference proceedings; see THIS LINK.Kadison and Ringrose's 'Fundamentals of the theory of operator algebras' was originally published by Academic Press in the1980s. This two-volume work(split into 'Elementary theory' and 'Advanced theory')met with immediate acclaim from functional analysts as a clear, careful, self-contained introduction to C*- and von Neumann algebra theory - an area in which it is notoriously easy to intimidate rather than initiate graduate students! Experts too relished the fresh gloss that the immensely experienced duo of authors brought to the development of the theory, and lecturers appreciated the large and eclectic set of exercises provided at the end of each chapter which reflected the authors' total familiarity with the literature.

Here is Kadison's own description of one such conference [3]:-

[Kadison received many honours for his outstanding contributions. For example he was elected to the National Academy of Sciences (1996), awarded an honorary degrees from the Université Aix-Marseille (1986) and the University of Copenhagen (1987), elected to the Royal Danish Academy of Sciences and Letters (1974), elected one of the Inaugural Class of Fellows of the American Mathematical Society (2013), and elected to the American Academy of Arts and Sciences (2018).I attended a conference at]University of Newcastle-on-Tyne in England[in June2001]. That conference, on Banach Algebras, was in honour of Barry Johnson, an heroic figure in that and allied subjects. There was a sadness about that meeting. Barry had terminal cancer and was near the end of his life. We all knew of Barry's mathematical heroism. On this occasion, we had the unhappy opportunity to note his physical courage as well. He attended a number of lectures, clearly with effort and in some pain, yet attentive and interested. Both he and Bill Arveson were at my lecture - paying close attention. I was speaking about some work I was doing related to the Pythagorean theorem - what is often referred to as the "converse"(if the numbers are right, there is a right triangle with sides of those lengths).

Not only was Kadison a member of the National Academy of Sciences but he was also a strong supporter. This was recognised by listing him in the Charter Society (those who have donated $1â000 to $10â000), in the Challenge Society (those who have donated $2,500 to $5,0000), in the Elkan Blout Society of the National Academy of Sciences (members of the National Academy of Sciences who have contributed $20â000 to $100â000), and in the Loyalty Society (in recognition of members and friends who have made gifts to the National Academy of Sciences for at least 20 years).

In 1999 Kadison was awarded the Leroy P Steele Prize for Lifetime Achievement by the American Mathematical Society. The citation begins [8]:-

For Kadison's response to receiving this award, see THIS LINK.The Leroy P Steele Prize for Lifetime Achievement is awarded to Richard V Kadison, Kuemmerle Professor of Mathematics at the University of Pennsylvania. For almost half a century, Dick Kadison has been one of the world leaders in the subject of operator algebras, and the tremendous flourishing of this subject in the last thirty years is largely due to his efforts. He was a key organizer of two major conferences on operator algebras - in Baton Rouge, Louisiana, in1967, and in Kingston, Ontario, in1980- which helped shaped the modern history of the subject. His students have included many world-class mathematicians not only in operator algebras but in other fields as well. And in mathematical exposition, Kadison's papers and his two-volume monograph with John Ringrose, 'Fundamentals of the Theory of Operator Algebras'(originally published by Academic Press, now reprinted by the AMS), have been models of clarity and precision.

On Saturday 10 January 2015, as part of their winter meeting, the American Mathematical Society held a 'Special Session on Operator Algebras and Their Applications: A Tribute to Richard V Kadison'.

Kadison died in August 2018 after a short illness. The University of Pennsylvania is organising a memorial conference, 'Operator Algebras in the 21st Century; Richard V Kadison Memorial Conference - 30-31 March 2019'. The conference website contains the following [1]:-

Starting in the middle1960s the University of Pennsylvania was known as a world centre of mathematics connected to the foundations of Quantum Physics, including functional analysis, operator algebras, von Neumann algebras, and group representation theory. At the centre of this research effort and the very distinguished group of mathematicians who pursued it was Richard V Kadison. Dick was the Gustave C Kuemmerle Professor in the Department of Mathematics from1964until his sudden, and unexpected death this past July. This truly marks the end of a long and distinguished chapter in the history of the Penn Mathematics department, and of the University as a whole, but by no means does it mark the end of Operator Algebras as vital field of Mathematics. Dick's passing provides an occasion for a meeting that will both celebrate his central role in the growth and vitality of this field, and explore its current state and future directions.

**Article by:** *J J O'Connor* and *E F Robertson*