# Donald E. Sarason

## Professor of Mathematics, Emeritus

Donald Erik Sarason was born in Detroit on January 26, 1933. He received his B.S. in physics in 1955 from the University of Michigan. He then studied medicine at Harvard, but returned to Michigan to pursue a master’s degree in physics (A.M., 1955). Don came to realize that his true calling was mathematics. He completed his Ph.D. in mathematics in 1963 at Michigan. His dissertation on Hardy spaces, supervised by Paul R. Halmos, was entitled “The *H ^{p}* spaces of annuli.” After a postdoctoral year at the Institute for Advanced Study, he joined the Berkeley faculty as assistant professor in 1964, serving until his retirement in 2012. He rose to associate professor in 1967, and to professor in 1970. He was awarded a National Science Foundation postdoctoral fellowship, and later a Sloan Research Fellowship (1969-1971). In 2003, and again in 2006, he was honored by the UC Berkeley Mathematics Undergraduate Student Association for outstanding undergraduate teaching. He served as Graduate Vice Chair of the Mathematics Department. He was a member of the Academic Senate’s Committee on the Status of Women and Ethnic Minorities (1974-75).

Don was a central figure in the department's very strong group of functional analysts. In his quiet way he was an ideal colleague, who generously shared his deep knowledge and wisdom with his colleagues and students alike. Don often taught the department's core graduate courses in functional and complex analysis, and so he trained not only many doctoral students who later did their research under his direction, but also many who then worked under the direction of his colleagues. Consequently, he was the second reader for a large number of doctoral theses, especially ones written under the direction of Bill Arveson, Vaughan Jones, Marc Rieffel, and Dan Voiculescu.

A stellar teacher and generous mentor, Don supervised a remarkable total of 40 Ph.D. dissertations, spanning a period of 40 years. The Mathematics Genealogy Project credits him with an extraordinary 250 professional descendants. Several of his Ph.D. students have become distinguished researchers in leading mathematics departments. Others have excelled as university administrators, or as researchers in other disciplines. He was as successful with those struggling to find their feet in research as with the most brilliant talents.

Don was famously succinct and direct. It was said by his teacher, Halmos, that Don would never use eight words when seven would suffice. Those words that did emerge were augmented by pauses. At the conclusion of a lecture by his former student David Cruz-Uribe, vindicating a research program proposed years earlier by the student, Don rose, said "David, you were right," and sat.

Don's research focused on operator theory, on complex function theory, and especially on the fruitful interaction between these two. He published approximately 76 mathematical papers over a full half century. While some 55 of Don's works were singly authored, he also collaborated with 25 co-authors.

Don served on the editorial boards of three professional journals, the Proceedings of the American Mathematical Society, Integral Equations and Operator Theory, and the Journal of Functional Analysis. He contributed nearly 500 article reviews to *Mathematical Reviews*, an astonishingly generous contribution of his time and expertise to the literature of his discipline. His thoroughness, in scholarship and in teaching, was exemplary.

Don's 1967 paper “Generalized interpolation in *H ^{∞}*” ignited a field pursued by researchers worldwide for decades. It introduced new techniques to the study of holomorphic interpolation problems and function algebras, and birthed commutant lifting theory.

His landmark 1975 paper “On functions of vanishing mean oscillation” introduced the space VMO, developed its properties, and delineated its connection with complex function theory. He brought to light a key property of the closed algebra *H ^{∞}* +

*C*generated by the holomorphic and the continuous bounded functions. The paper became a cornerstone in the development of the theory of Douglas algebras, and led to their eventual characterization by S-Y. A. Chang (Don's former student) and D. Marshall. Don's expertise on

*H*led, in the hands of his student J. Doyle, to applications to control theory in engineering, and thence to four academic grandchildren on the UCB engineering faculty.

^{∞}Don's 1978 lecture notes *Function Theory on the Unit Circle*, based on a lecture series given at the Virginia Polytechnic Institute and State University, were never formally published, yet are his fourth-most cited work on Google Scholar. They influenced experts, and became an important text for Don's students. In the 1990s, Don's interest turned to Hilbert spaces in complex analysis and to reproducing kernels and connections with Toeplitz operators. His 1994 book *Sub-Hardy Hilbert Spaces in the Unit Disk* developed the theory of the de Branges–Rovnyak spaces. Don also authored the characteristically pristine undergraduate textbook *Complex Function Theory*.

For decades, Don was a fixture in Evans Hall, climbing the stairs daily to his seventh floor office, invariably clad in jeans and plaid shirt, with long beard and longer ponytail. He was gifted with a very dry sense of humor, which he was wont to exercise in class. A famous story tells about his response to a rare comment in a student evaluation that his dress was too casual for a professor, particularly without a tie. Don’s remedy was to set about collecting remarkably unappealing second-hand ties. He kept them on a coat rack in his office. On his way out the door to lecture, he would select a tie that that would clash with whatever shirt he was wearing. Over the years, the tie collection grew, enhanced by contributions from students who shared his views on formal wear.

On another occasion, while addressing a distinguished conference audience at the University of Chicago, Don felt compelled to explain, with his trademark deadpan delivery, that despite his appearance and Berkeley affiliation, he was actually a rather conservative person.

Don enjoyed jogging, cooking, reading the *New York Times*, and retrieving lost coins from risky locations on walks with his wife, Mary – over the years, they accumulated the tidy sum of more than $800!

He passed away at home on April 8, 2017 after an extensive period of illness. He is survived by his loving wife of 27 years, Mary Jennings, son Benjamin, stepchildren Anne Marie Jennings, Allison Jennings, Herbert Jennings, and Daniel Jennings, and by his sisters Constance Grossman and Judith Sarason, brother Thomas Sarason, and by three step-grandchildren. A memorial by three of Don's students was published in the *Notices** of the American Mathematical Society*, Vol. 65, 2018, pp.195-200.

Don Sarason's unique kindness, gentleness, and generosity left a mark on all who knew him.

Michael Christ

2020