Standard operator models in the polydisc, II

Standard Operator Models in the Polydisc, II

We first show that every γ-contractive commuting multioperator is unitarily equivalent to the restriction of S⊕W to an invariant subspace, where S is a backwards multi-shift and W a γ-isometry. We then describe γ-isometries in terms of (γ, 1)-isometries, and establish that under an additional assumption on T , W above can be chosen to be a commuting multioperator of isometries. Our methods prov...

Multiplicative bijective maps on standard operator algebras

Interpolating Sequences in the Polydisc

Let H°°(Dn) denote the set of all bounded analytic functions defined on the polydisc D" of Cn. In this note, we give a sufficient condition for sequences of points in £>" to be interpolating sequences for H°°(Dn). We also discuss some conditions for interpolation of general domains. Let G(X) be the set of all bounded continuous functions on a compact set X and let A C C(X) be a uniform algebra ...

The //"-corona Theorem for the Polydisc

Let Hp = Hp(D") denote the usual Hardy spaces on the polydisc D" . We prove in this paper the following theorem: Suppose f\, fa, ... , fit € H°° , \\fj\\Hoo <\,and Y.%\ \fj(z)\ > S > 0. Then for every g in HP , 1 < p < oo, there are Hp functions g, g, ... , gm such that 2~2T=\ fj(z)Sj(z) = g(z). Moreover, we have ||g/||//p < c(m, n, S , p)\\g\\np . (When p = 2, n = 1 , this theorem is known to ...

Positive Carath Eodory Interpolation on the Polydisc

The positive Carath eodory interpolation problem in the Agler-Herglotz class on the polydisc is solved, along with a several variable version of the Naimark dila-tion theorem. In addition, the positive Carath eodory interpolation problem for general holomorphic functions is discussed and numerical results are presented.