David Borwein Distinguished Career Award and Lecture
 KENNETH R. DAVIDSON, University of Waterloo
Noncommutative dilation theory [PDF]

Dilation theory of a single operator began in 1953 with Bela Sz.Nagy's result that
every operator on Hilbert space with norm at most 1 is the upper corner of a 2x2
lower triangular operator matrix which is an isometry. This led to a powerful functional
calculus for studying a single operator on Hilbert space. In 1968, William Arveson
set out a general theory for studying nonselfadjoint subalgebras of C*algebras through their
representation theory, and the main pillar was a generalization of the Sz.Nagy dilation
theory. In the past four decades, these ideas have been developed into a major tool
for studying these algebras. I will survey some of these ideas.