Operator positivity and analytic models of commuting tuples of operators

摘要

We study analytic models of operators of class C-.0 with natural positivity assumptions. In particular, we prove that for an m-hypercontraction T is an element of C-.0 on a Hilbert space H, there exist Hilbert spaces epsilon and epsilon(*) and a partially isometric multiplier theta is an element of M(H-2 (epsilon), A(m)(2) (epsilon(*))) such that