William Barnes Arveson A longtime member of the mathematics faculty at the University of California in Berkeley, died in Berkeley on November 15 due to complications from anesthesia during surgery. Bill was 76. He was born in Oakland, CA. In his youth, Bill served on an aircraft carrier as a radar technician in the US Navy, and worked at the Naval Undersea Research and Development Center. He was a graduate of the California Institute of Technology and received his PhD from

UCLA (both funded by the Navy). Bill was a Benjamin Peirce Instructor at

Harvard University, and since 1968 was at UC Berkeley where he was a Professor of Mathematics. He had visiting positions in the US and world-wide, including UCLA, UCSD, Pennsylvania, Newcastle (UK), Aarhus (Denmark), Oslo and Trondheim (Norway), Stockholm, Tel Aviv, Canberra, Rio de Janeiro, Tianjin (China), and Kyoto. He also received two Miller research professor awards at Berkeley. Bill strongly inspired and influenced many researchers through his teaching, writing, and lecturing. An elegant expositor who took great care with his writing, he published 79 scholarly manuscripts and authored eight books on C*-algebras, operator algebras, spectral theory, and noncommutative dynamics. His editorial services included the Bulletin of the American Mathematical Society, Proceedings of the Edinburgh Mathematical Society, Duke Mathematical Journal, and three decades as Editor of the Journal of Operator Theory (Romania). Always generous with his time, Bill was committed to the mentorship of young mathematicians, of whom 29 wrote their doctoral dissertations under his guidance. Many of them went on to be prominent research mathematicians in their own right. Bill was a leading expert and a highly innovative researcher in his field, an area of mathematics that underlies quantum physics and can be traced back to Heisenberg's formulation of quantum mechanics. He made many surprising discoveries, continuing to do so until nearly the end of his life. Some of his early work was only fully appreciated years after its publication. Bill pioneered the exploration of certain mysterious structures that arise in a basic way from the modeling of the irreversible dynamics of quantum systems, for example, the creation and annihilation of particles such as electrons and the strange particles found in cosmic rays. In the 1990's he opened a new front in his research, with highly original ideas for applying seemingly unrelated "abstract" mathematics to the efficient calculation of important quantities in quantum physics. During the past decade Bill's important contributions continued to flow as strongly as ever, and began to include applications of quantum spaces to quantum information theory and quantum computing. Bill loved jazz and the movies. Bill is survived by his wife of 26 years, Lee Ann Kaskutas, by his sons Jeff and Robert from a previous marriage, and by his miniature dachshund Bronco. All will miss him dearly, as will scores of fellow mathematicians who worked with him, learned from him, and were inspired by him.