William Arveson

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William Arveson (born 22 November 1934 in Oakland, California) is a mathematician specializing in operator algebras. He is currently professor of Mathematics at the University of California, Berkeley. Arveson obtained his Ph. D. from 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^[1]. 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.

Arveson's paper ^[2] on non-selfadjoint algebras is one of the most cited papers in Operator theory. It is celebrated by experts both for its results on the reflexivity of certain lattices and the techniques introduced, which have inspired decades of research.

[edit] Notes

1. ^ Subalgebras of $C\sp{*} $-algebras, Acta Math, 123 (1969), 141--224
2. ^ Operator algebras and invariant subspaces, Annals of Math.(2), 100 (1974), 433--532

[edit] External links

• Directory of operator theorists

California school stubs