William Arveson
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William Arveson is a mathematician specializing in operator algebras. He is currently professor of Mathematics at the University of California, Berkeley. Arveson obtained his Ph. D. at UCLA in 1964.
Of particular note is Arveson's work on completely positive maps. One of his earlier results in this area is an extension theorem for completely positive maps with values in the algebra of all bounded operators on a Hilbert space. This theorem led naturally to the question of injectivity of von-Neumann algebras in general, which culminated in work by Alain Connes relating injectivity to hyperfiniteness.
