Dilation Theory and Systems of Simultaneous Equations in the Predual of an Operator Algebra. II

1. This note is a continuation of our earlier paper [-3], in which we developed a dilation theory for a certain class of contraction operators acting on a separable, infinite dimensional, complex Hilbert space ~ . The notation and terminology in what follows is taken from [3]. For the convenience of the reader we recall a few pertinent definitions. The algebra of bounded linear operators on ~ is denoted by Y ( ~ ) . If T~Se(2C), the ultraweakly closed algebra generated by T and l~e is denoted by dr; we recall that d r can be identified with the dual space of the quotient space Q r = ( z c ) / • where (zc) denotes the ideal of trace-class operators in 5~(24 ~) and • is the preannihilator of d r in (z c), under the pairing