 
Summary: SUBALGEBRAS OF C
ALGEBRAS III:
MULTIVARIABLE OPERATOR THEORY
William Arveson
Department of Mathematics
University of California
Berkeley CA 94720, USA
18 May 1997
Abstract. A dcontraction is a dtuple (T1, . . . , Td) of mutually commuting opera
tors acting on a common Hilbert space H such that
T11 + T22 + · · · + Tdd
2
1
2
+ 2
2
+ · · · + d
2
for all 1, 2, . . . , d H. These are the higher dimensional counterparts of contrac
tions. We show that many of the operatortheoretic aspects of function theory in the
